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1. MARIAN 2004 - Nonstandard Models Of Arithmetic And Analysis The common ground of Nonstandard models justifies a congress aimed to bring together researchers working on Peano Arithmetic and on Nonstandard analysis. http://www.dm.unipi.it/~dinasso/marian2004/

HOME PROGRAM ABSTRACTS HOTELS MAP International Congress M.ARI.AN. 2004 Nonstandard Models of Arithmetic and Analysis June 25-26, 2004, Pisa. Scientific Committee: Mauro Di Nasso (Univ. Pisa), Marco Forti (Univ. Pisa), Karel Hrbacek (CUNY, New York), Roman Kossak (CUNY, New York) Organizer: Mauro Di Nasso (Univ. Pisa, Italia) General information The study of Peano Arithmetic and its sub-theories, involves several different topics in mathematical logic, namely model-theory, definability, complexity. Nonstandard analysis is one of the most relevant applications of model theory. It provides a sound mathematical basis for the use of infinitesimal and infinite numbers in analysis. The study of the so-called "nonstandard methods", on the one side originated interesting foundational issues, on the other side provided a useful tool in applications. The common ground of "nonstandard models" justifies a congress aimed to bring together researchers working on Peano Arithmetic and on nonstandard analysis.

2. Nonstandard Models And Kripke S Proof Of The Gödel Theorem Today we know purely algebraic techniques that can be used to give direct proofs of the existence of Nonstandard models in a style with which ordinary http://projecteuclid.org/handle/euclid.ndjfl/1027953483

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Hilary Putnam Source: Notre Dame J. Formal Logic Volume 41, Number 1 (2000), 53-58. Abstract Primary Subjects: Secondary Subjects: Keywords: models of arithmetic; nonstandard models of arithmetic Full-text: Access granted (open access) Screen Optimized PDF File (192 KB) PDF File (189 KB) Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1027953483 Digital Object Identifier: doi:10.1305/ndjfl/1027953483 Zentralblatt Math identifier: back to Table of Contents previous next Notre Dame Journal of Formal Logic Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

3. OUP: UK General Catalogue This is the proceedings of the AMS special session on Nonstandard models of arithmetic and set theory held at the Joint Mathematics Meetings in Baltimore http://www.oup.com/uk/catalogue/?ci=9780821835357

4. Automated Fitting Of Nonstandard Models. EJ453868 Automated Fitting of Nonstandard models. http://www.eric.ed.gov/ERICWebPortal/recordDetail?accno=EJ453868

5. Automated Fitting Of Nonstandard Models A method for automated parameter estimation and testing of fit of Nonstandard models for mean vectors and covariance matrices is described. http://www.questia.com/PM.qst?a=o&se=gglsc&d=96241821

6. JSTOR Nonstandard Models And Related Developments. Nonstandard models and related developments. Ibid., pp. 179229. In his contribution to the volume, the author gives an exposition of H. Friedman s http://links.jstor.org/sici?sici=0022-4812(199006)55:2<875:NMARD>2.0.CO;2-B

7. [math/0209408] Satisfaction Classes In Nonstandard Models Of First-order Arithme Satisfaction classes in Nonstandard models of firstorder arithmetic. Authors Fredrik Engström Comments Thesis for the degree of licentiate of philosophy, http://arxiv.org/abs/math/0209408

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PostScript PDF Other formats Citations CiteBase p revious n ... ext Mathematics > Logic Title: Satisfaction classes in nonstandard models of first-order arithmetic Authors: (Submitted on 30 Sep 2002) Abstract: A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively saturated. A proof of this fact is presented in detail in such a way that it is adaptable to a language with function symbols. The idea that a satisfaction class can only see finitely deep in a formula is extended to terms. The definition gives rise to new notions of valuations of nonstandard terms; these are investigated. The notion of a free satisfaction class is introduced, it is a satisfaction class free of existential assumptions on nonstandard terms. It is well known that pathologies arise in some satisfaction classes. Ideas of how to remove those are presented in the last chapter. This is done mainly by adding inference rules to M-logic. The consistency of many of these extensions is left as an open question.

8. Nonstandard Models Of Arithmetic On The Web Furthermore, it has a model of every cardinality greater than or equal to aleph_0. This theorem established the existence of Nonstandard models of http://www.log24.com/log05/051023-Nonstd.html

Nonstandard Models of Arithmetic on the Web (Mathematics Subject Classification 2000: 03H15, Nonstandard models of arithmetic) Notes by Steven H. Cullinane on Oct. 23, 2005 The Mathematical Experience by Philip J. Davis and Reuben Hersh: "It was discovered by the Norwegian logician Thorolf Skolem that there are mathematical structures which satisfy the axioms of arithmetic, but which are much larger and more complicated than the system of natural numbers. These 'nonstandard arithmetics' may include infinitely large integers. In reasoning about the natural numbers, we rely on our complete mental picture of these numbers. Skolem's example shows that there is more information in that picture than is contained in the usual axioms of arithmetic." Non-Standard Models in a Broader Perspective by Haim Gaifman (pdf) Non-Standard Models of Arithmetic by Asher M. Kach (pdf) MathWorld Nonstandard Models of Arithmetic by Ali Lloyd (pdf)

9. Model Independent Analysis We decided some time ago to analyze the data in as model independent a context as possible 9,51. Though most explicitlyconstructed Nonstandard models http://www.physics.upenn.edu/neutrino/sun-nu/node6.html

Next: Neutrino Oscillations Up: Astrophysical Solutions Previous: Cool Sun Models Model Independent Analysis We decided some time ago to analyze the data in as model independent a context as possible [ ]. Though most explicitly-constructed nonstandard models involve either the temperature or the cross sections [ ] there is always the possibility of very nonstandard physical inputs which cannot be described in this way. The idea in a model independent analysis is that all that really matters for the neutrinos are the magnitudes and of the various flux components. We can then analyze the data making only three minimal assumptions. One is that the solar luminosity is quasi-static and generated by the normal nuclear fusion reactions. This leads to the constraints ( ) and ( ). The second assumption is that astrophysical mechanisms cannot distort the shape of the spectrum significantly from what is given by normal weak interactions. Nobody has found any astrophysical mechanism that can significantly distort the shape, and all explicitly studied mechanisms are negligibly small [ ]. It is this assumption which differentiates astrophysical mechanisms from MSW, which can distort the shape significantly. Our third assumption is that the experiments are correct, as are the detector cross section calculations.

10. Open Arithmetic And Its Nonstandard Models Open arithmetic and its Nonstandard models. Source, Journal of Symbolic Logic archive Volume 56 , Issue 2 (June 1991) table of contents. Pages 700 714 http://portal.acm.org/citation.cfm?id=120276.120298

11. Buy.com - The Structure Of Nonstandard Models Of Arithmetic : Roman Kossak : ISB The Structure of Nonstandard models of Arithmetic Roman Kossak ISBN 9780198568278 Book. http://www.buy.com/prod/the-structure-of-nonstandard-models-of-arithmetic/q/loc/

My Account Wishlist Help All Departments ... Warranties Books by Title by Author by ISBN by Publisher Buy.com Save $30 Instantly with the Buy.com Visa Card. Click here. Books Best-sellers New ... Rewards UpdateProductViewHistoryCookie('The Structure of Nonstandard Models of Arithmetic','202779808'); The Structure of Nonstandard Models of Arithmetic (Hardcover) Author: Roman Kossak Jim Schmerl Product Image Pricing Additional Info FREE SHIPPING Our Price: Shipping FREE Buy.com Total Price: Qty Temporarily Sold Out. More inventory may be available. Place your order today and be one of the first to receive this product when it arrives! Alert me when this item is in stock. Format: Hardcover See 1 New for What's this? Format: Hardcover ISBN: Publish Date: Publisher: Oxford University Press Dimensions (in Inches) 9.25H x 6.25L x 0.75T Pages: Buy.com Sku: More about this product Item#: View similar products Product Summary Reviews Aimed at research logicians and mathematicians, this much-awaited monograph covers over forty years of work on relative classification theory for non-standard models of arithmetic. With graded exercises at the end of each chapter, the book covers basic isomorphism invariants: families of types realized in a model, lattices of elementary substructures and automorphism groups. Many results involve applications of the powerful technique of minimal types due to Haim Gaifman, and some of the results are classical but have never been published in a book form before.

12. Philosophia Mathematica -- Sign In Page The Nonstandard models of arithmetic are definitely not intended models. Thus Nonstandard models are simply ruled out by this restriction on the http://philmat.oxfordjournals.org/cgi/content/full/13/2/174

@import "/resource/css/hw.css"; @import "/resource/css/philmat.css"; Skip Navigation Oxford Journals Contact Us My Basket ... Volume 13, Number 2 Pp. 174-186 This item requires a subscription* to Philosophia Mathematica Online. * Please note that articles prior to 1996 are not normally available via a current subscription. In order to view content before this time, access to the Oxford Journals digital archive is required. If you would like to purchase short-term access you must have a personal account. Please sign in below with your personal user name and password or register to obtain a user name and password for free. Full Text Computational Structuralism Halbach and Horsten Philosophia Mathematica. To view this item, select one of the options below: Sign In User Name Sign in without cookies. Can't get past this page? Help with Cookies. Need to Activate? Password Forgot your user name or password? Purchase Short-Term Access Pay per View - If you would like to purchase short-term access you must have a personal account. Please sign in with your personal user name and password or register to obtain a user name and password for free. You will be presented with Pay per Article options after you have successfully signed in with a personal account.

13. MSC2000 03H10 Other applications of Nonstandard models (economics, physics, etc. 03H15 Nonstandard models of arithmetic Other Nonstandard models ( 0 Dok. http://archiv.ub.uni-marburg.de/opus/msc_ebene3.php?zahl=03H&anzahl=0&la=de

14. EMail Msg <199311032226.AA12544@dante.cs.uiuc.edu> (What they might be able to do, should we become embroiled in a debate, is show me that on my interpretation there are Nonstandard models of arithmetic, http://www-ksl.stanford.edu/email-archives/interlingua.messages/412.html

phayes@cs.uiuc.edu Mail folder: Interlingua Mail Next message: Harold Boley: "Re: Higher-order KIF & CGs" Previous message: Fritz Lehmann: "Re: Higher-order KIF & CGs" Maybe in reply to: Fritz Lehmann: "Re: Higher-order KIF & CGs" Reply: Harold Boley: "Re: Higher-order KIF & CGs" Message-id:

15. 03: Mathematical Logic And Foundations The construction of Nonstandard models for certain sets of axioms leads to Nonstandard analysis of those axioms. In particular, a Nonstandard model of the http://www.math.niu.edu/~rusin/known-math/index/03-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 03: Mathematical logic and foundations Introduction Mathematical Logic is the study of the processes used in mathematical deduction. The subject has origins in philosophy, and indeed it is only by nonmathematical argument that one can show the usual rules for inference and deduction (law of excluded middle; cut rule; etc.) are valid. It is also a legacy from philosophy that we can distinguish semantic reasoning ("what is true?") from syntactic reasoning ("what can be shown?"). The first leads to Model Theory, the second, to Proof Theory. Students encounter elementary (sentential) logic early in their mathematical training. This includes techniques using truth tables, symbolic logic with only "and", "or", and "not" in the language, and various equivalences among methods of proof (e.g. proof by contradiction is a proof of the contrapositive). This material includes somewhat deeper results such as the existence of disjunctive normal forms for statements. Also fairly straightforward is elementary first-order logic, which adds quantifiers ("for all" and "there exists") to the language. The corresponding normal form is prenex normal form. In second-order logic, the quantifiers are allowed to apply to relations and functions to subsets as well as elements of a set. (For example, the well-ordering axiom of the integers is a second-order statement). So how can we characterize the set of theorems for the theory? The theorems are defined in a purely procedural way, yet they should be related to those statements which are (semantically) "true", that is, statements which are valid in every model of those axioms. With a suitable (and reasonably natural) set of rules of inference, the two notions coincide for any theory in first-order logic: the Soundness Theorem assures that what is provable is true, and the Completeness Theorem assures that what is true is provable. It follows that the set of true first-order statements is effectively enumerable, and decidable: one can deduce in a finite number of steps whether or not such a statement follows from the axioms. So, for example, one could make a countable list of all statements which are true for all groups.

16. Non-standard Models Of PA - Sci.logic | Google Groups Countable Nonstandard models of PA all have this structure. Torkel Franzen wrote Right, but this doesn t define any model. Aww, come ON! http://groups.google.co.ls/group/sci.logic/msg/062ecc41156e58c9

Help Sign in sci.logic Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Non-standard models of PA The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful george View profile More options Sep 1 2005, 1:37 am Newsgroups: sci.logic From: "george" <gree Date: 31 Aug 2005 16:37:02 -0700 Local: Thurs, Sep 1 2005 1:37 am Subject: Re: Non-standard models of PA Reply to author Forward Print View thread ... Find messages by this author Torkel Franzen wrote: Aww, come ON! These models are NOT RECURSIVE! They canNOT HAVE finitary "definitions"! The structure as described here DOES define the How COULD you further ASK anyone to "define" its + and x WHEN YOU KNOW that they are not recursive "This" defines as much of these models as CAN be defined, at a first pass. One could propound further finitary approximations of + and x in these models

17. Ultrafilters, Nonstandard Analysis, And Epsilon Management « What’s New With this we can now discuss nonstandard models of a mathematical system. There are a number of ways to build these models, but we shall stick to the most http://terrytao.wordpress.com/2007/06/25/ultrafilters-nonstandard-analysis-and-e

Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao Home About Career advice On writing ... Subscribe to feed Ultrafilters, nonstandard analysis, and epsilon management 25 June, 2007 in expository math.CA math.LO opinion Tags: epsilon management hard analysis Landau notation nonstandard analysis ... ultrafilters This post is in some ways an antithesis of my previous postings on hard and soft analysis that one needs to manage, in particular choosing each epsilon carefully to be sufficiently small compared to other parameters (including other epsilons), while of course avoiding an impossibly circular situation in which a parameter is ultimately required to be small with respect to itself, which is absurd. This art of epsilon management Heine-Borel theorem One important step in this direction has been the development of various types of asymptotic notation , such as the Hardy notation of using unspecified constants C, the Landau notation or axiom schema of specification , and so the above definition of A is meaningless. non-standard analysis ultrafilter (or an equivalent gadget), which tends to deter people from wanting to hear more about the subject. Because of this, most treatments of non-standard analysis tend to gloss over the actual

18. Higher Order Logic And Nonstandard Models Henkin (1950) developed a notion of general model that included nonstandard as well as standard models. In the general setting, it is possible for D to http://www.lix.polytechnique.fr/Labo/Dale.Miller/papers/AIencyclopedia/

A short article for the Encyclopedia of Artificial Intelligence : Second Edition by Dale Miller, February 1991 While first-order logic has syntactic categories for individuals, functions, and predicates, only quantification over individuals is permitted. Many concepts when translated into logic are, however, naturally expressed using quantifiers over functions and predicates. Leibniz's principle of equality, for example, states that two objects are to be taken as equal if they share the same properties; that is, a b P P a P b )]. Of course, first-order logic is very strong and it is possible to encode such a statement into it. For example, let app be a first-order predicate symbol of arity two that is used to stand for the application of a predicate to an individual. Semantically, app P x ) would mean P satisfies x or that the extension of the predicate P contains x P app P a app P b )] (appropriate axioms for describing app app . Higher-order logics arise from not doing this kind of encoding: instead, more immediate and natural representation of higher-order quantification are considered. Indeed naturalness of higher-order quantification is part of the reason why higher-order logics were initially considered by Frege and Russell as a foundation for mathematics. SYNTAX OF HIGHER-ORDER LOGIC i.e.

19. Application Scenarios For Nonstandard Log-linear M...[Psychol Methods. 2007] - P Second, application scenarios are presented for nonhierarchical and Nonstandard models, with illustrations of where these scenarios can occur. http://www.ncbi.nlm.nih.gov/sites/entrez?db=pubmed&uid=17563169&cmd=showdetailvi

20. 80-611 Computability And Incompleteness INSTRUCTOR Jeremy Avigad It is shown that theories which have infinite models must have Nonstandard models. Henkin s Completeness Theorem is proved. Attention then turns to showing http://logic.cmu.edu/pal-courses-s08.txt

21-803 Math Logic Seminar INSTRUCTOR: James Cummings R 12-1:20 Doherty Hall 1217 DESCRIPTION: See http://logic.cmu.edu/seminar.html 21-805 Unification and Matching in Typed Lambda Calculus INSTRUCTOR: Rick Statman MWF 3:30-4:20 (this course will probably move to a TR time slot) Doherty Hall 2122 12 Units 15-812A Programming Language Semantics INSTRUCTOR: John C. Reynolds MW 1:30-2:50 Wean Hall 4615A 12 units DESCRIPTION: We survey the theory behind the design, description, and implementation of programming languages, and of methods for specifying and verifying program behavior. Both imperative and functional programming languages are covered, as well as ways of integrating these paradigms into more general languages. Coverage will include: - program specification and proof (including Hoare logic, weakest preconditions, and separation logic) - concurrent programming (including shared-variable and message-passing approaches) - functional programing (including continuations and lazy evaluation) - type systems (including subtyping, polymorphism, and modularization) In exploring these topics, we will use a variety of fundamental concepts and techniques, such as compositional semantics, binding structure, domains, transition systems, and inference rules. PREREQUISITES: There are no specific prerequisites, but the course requires some background in programming languages and basic mathematics. To get a feel for what is needed look at Appendix A of the text and skim over the first couple of chapters. If these seem unduely difficult, meet with the instructor. TEXTBOOK: J. C. Reynolds, "Theories of Programming Languages", Cambridge University Press 1998. WEB PAGE: /afs/cs.cmu.edu/project/fox-19/member/jcr/www15812As2008/cs812-08.html 80-619 Computability and Learnability Instructor: Kevin Kelly TR 1:30-2:50 BH A53 Baker Hall A53 12 Units Description: This course is conceived as an alternative way to fulfill the 80-311, Computability and Incompleteness requirement for students who are more interested in rationality, learning, and scientific method than in logic and the foundations of mathematics. A solid grounding in the theory of computability will be provided, but the applications will concern computational learning theory, which studies what can be learned or discovered by computational agents from empirical data rather than what can be proved in a logical system. The application is more natural than it might seem at first. The problem of induction is that a general law may be refuted by the next observation, no matter how long it has withstood test. But there is a parallel problem about algorithmic halting: no matter how long a computation fails to halt, it may halt as soon as a world-be decision procedure concludes that it never will. In both cases, the difficulty can be sidestepped by entertaining methods that converge to the right answer without announcing when they have done so. We will delve into this analogy, using the theory of computability to investigate such questions as what machines can learn, whether machines could discover uncomputable truths, why irrational machines may be smarter, and what good it would do to have an infinite regress of methods, each of which checks whether its predecessor will find the truth. All topics covered are self-contained, but students are expected to have some basic background in logic, computation, or discrete mathematics. The text will consist of handout lecture notes. The course grade will be based on exercises and two short papers that will provide vital practice in writing articles for conference proceedings.

21. Set Theory Meeting In Amstedam In August 2007 For many set theorists, Nonstandard models of ZF are pathological and devoid of serious mathematical interest. To correct this view, I will present a http://staff.science.uva.nl/~ikegami/Ams_Aug_2007.html

Set Theory Meeting in Amsterdam in August 2007 Date: August 13th (Mon.) Place: P-017 (The Euclides building ) Time schedule: 10:00-10:30 Coffee and cookies Peter Koepke , "Sets in Prikry Extensions" 11:30-13:00 Lunch Joel David Hamkins , "There is no nontrivial elementary embedding from one ground model to another" 14:00-14:15 Break Luca Motto Ros , "A dichotomy theorem for Borel reducibilities " 15:15-15:30 Break Brian Semmes , "Jayne-Rogers with Games" 16:30-16:45 Break Ali Enayat , "In praise of nonstandard models" Break Philip Welch, TBA Abstracts Peter Koepke Title "Sets in Prikry Extensions" Abstract. Prikry cofinal subseteq Prikry extension $V[C equiconstructible subseteq subseteq subseteq V[C subseteq C$. ( joint work with Vladimir Kanovei Moscow Joel David Hamkins Title "There is no nontrivial elementary embedding from one ground model to another" Abstract. Kunen's famous inconsistency theorem shows that there is no nontrivial elementary embedding j :V to V. This was extended by

22. Oxford Scholarship Online: The Structure Of Models Of Peano Arithmetic Abstract This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of Nonstandard models of http://www.oxfordscholarship.com/oso/public/content/maths/9780198568278/toc.html

About OSO What's New Subscriber Services Help ... Mathematics Subject: Mathematics Book Title: The Structure of Models of Peano Arithmetic The Structure of Models of Peano Arithmetic Kossak, Roman , City University of New York Schmerl, James , University of Connecticut, Storrs Print publication date: 2006 Published to Oxford Scholarship Online: September 2007 Print ISBN-13: 978-0-19-856827-8 doi:10.1093/acprof:oso/9780198568278.001.0001 Abstract: This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, and the important particular case of countable recursively saturated models is discussed in detail. All necessary technical tools are developed. The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's generic automorphisms; and applications of Abramson and Harrington's generalization of Ramsey's theorem. There are also chapters discussing 1-like models with interesting second order properties, and a chapter on order types of nonstandard models.

23. Making Sunshine Solaroscillation data have already ruled out several proposed Nonstandard solar models. As these data get better- particularly for conditions near the http://goodfelloweb.com/nature/cgbi/sn102889.html

Science News, 10/28/89 pp.280-281. Making Sunshine by Ivars Peterson What Makes the sun shine? According to the standard solar model, the nuclear engine at the sun's center pumps out a tremendous amount of energy. In this high temperature. high-pressure environment. protons (the nuclei of hydrogen atoms) fuse to create deuterons (proton neutron pairs). which then combine with protons or other deuterons to produce heavier atomic nuclei. and so on. Each step in this chain of nuclear fusion reactions releases energy. But something may be fundamentally wrong with this picture. Theoretical calculations, based on the types of nuclear reactions expected at the sun's core, indicate the sun should emit about 2 percent or its energy in the form of neutrinos- elusive particles that interact only feebly with matter. Yet the number of solar neutrinos actually detected at Earth's surface appears significantly smaller than theory predicts. The case of the missing solar neutrinos ranks as arguably the most puzzling problem in astrophysics. Is there a basic flaw in the theory of how stars generate energy? Or do neutrinos behave in peculiar ways not yet understood? Solar-neutrino experiments now in progress and others soon to start will probably settle these questions in the next few years. "The whole subject is coming together experimentally and theoretically," says John N. Bachall of the Institute for the advanced study in Prinston, N.J. "We're clearly at a time of very rapid change."

24. Table Of Contents Structure of Nonstandard models of Arithmetic (R. Kossak) This is a two year grant to support preparation of the book with the same title. http://www.bcc.cuny.edu/MathematicsComputerScience/listofgrants.htm

Department of Mathematics and Computer Science Undergraduate Research Faculty Tutoring and Computer Labs ... Math requirement for curriculum Grants and Special Projects Table of Contents Madelaine Bates and Roman Kossak Graphing Workshops Presidential Faculty Staff Development Grant (2000) Susan Forman Mathematics in Advanced Technological Education (ATE) Programs NSF-sponsored project (1999) Roman Kossak CUNY Logic Workshop Faculty Development Program Grant from the Office for Instructional Technology and External Programs of CUNY Graduate Center. (1998-2000) Structure of Nonstandard Models of Arithmetic / PSC-CUNY Grant Maria Psarelli Riemannian Manifolds associated with two step nilpotent Lie groups (With A. Koranyi, Distinguished Professor, Z. Szabo, Professor, Lehman College, M.Moskowitz, Graduate Center)/ CUNY Collaborative Research Grant 2000-2002 Asymptotic Behavior of Maxwell-Klein-Gordon Equations in 4-d Minkowski Space PSC-CUNY Research Grant, 2000-2002 Anthony Weaver Automorphisms of Riemann Surfaces PSC-CUNY Grant (1999) Peter Yom A Relationship between Vertices and Quasi-isomorphisms for a Class of Bracket Groups PSC-CUNY Grant (1999) On Quasi-representing Graphs for a Class of Butler Groups / PSC-CUNY Grant (2000) Abstracts Graphing Workshop ( : During the workshops, students explore the relation between a function and its graph using graphing calculator.

25. Tortorelli: A Characterization Of Internal Sets We shall call these models Nonstandard strong models. . An ZAstructure A is ac Nonstandard model if i) there exits in f inite natural numbers http://www.numdam.org/numdam-bin/item?id=RSMUP_1989__81__193_0

26. Another View Of Nonstandard Analysis In 1961, Abraham Robinson based a new way to study limits, continuity, and other aspects of analysis on Thoralf Skolem s Nonstandard models for Peano http://www.haverford.edu/math/wdavidon/NonStd.html

Another View of Nonstandard Analysis William C. Davidon, Haverford College, Haverford PA 19041 wdavidon@haverford.edu ... there are good reasons to believe that nonstandard analysis, in some version or other, will be the analysis of the future. 0. Introduction All versions of nonstandard analysis relate standard numbers to others in much the way that numbers like 1/7 and used in exact and symbolic computations relate to numbers like .142857 and 3.14159 used in numerical approximations. While nonstandard integers are too large to be uniquely specified, each has a decimal representatiion with a nonstandard number of digits, and students can compute with these in much the way that they do with standard integers, without reference to any formal theory; e.g. = 97...361. Each nonstandard positive integer exceeds all standard ones, and each has the familiar arithmetic properties of all standard integers; e.g. , each is a product of primes and a sum of four squares. Some mathematicians use Edward Nelson's Internal Set Theory [1977] to classify both standard and nonstandard integers as finite, and hence members of the ordered ring Z of finite integers. Others use a more traditional set theory to classify nonstandard integers as neither finite nor members of

27. Colloquium Talks Archive We outline an algebraic construction of Nonstandard models of the real numbers with exponentiation. These Nonstandard models provide useful asymptotic http://www.csudh.edu/math/wpong/wmc/02-04.html

CSUDH Math Colloquium 2002-2004 Ioana Mihaila (Cal Poly Pomona) Periodic Functions are a common occurrence in mathematics, but on the punctured complex plane we can actually consider multiplicative periodic functions. Can these functions be explicitly constructed, and are they useful? Jennifer Switkes (Cal Poly Pomona) On the Means of Deterministic and Stochastic Populations Familiar results for differential equation birth-death-immigration-emigration population models are compared with the expected population sizes predicted by related stochastic models. Although under standard assumptions the results are not equivalent, by removing certain restrictive modeling assumptions the two types of models can be reconciled. Terry Millar (University of Wisconsin Madison) Logic and Mathematics Terry Millar will talk about the role of logic in mathematics and will give two examples relevant to education. The first example will be from propositional logic and will be from a 4-5th grade class. The second example will deal with the definition of continuity and the use of infinitesimals. For both examples he will mention the complete and soundness theorems - for propositional and predicate logic, respectively. He also will mention a useful consequence - the compactness theorem - that can be used to introduce infinitesimals in a rigorous manner. Mona Mocanasu (UCLA) On the Milnor Conjecture In 2002 V. Voevodsky was awarded the Fields Medal for his development of a new homotopy and cohomology theory for algebraic schemes; a consequence of this construction is the proof of the Milnor Conjecture, a problem that awaited a solution for twenty-six years. The aim of this talk is to give a description of the conjecture, explain how it works in a couple of particular cases, and give an outline of Voevodsky¡¦s proof.

28. FOM: Non-standard Models, Completeness, Compactness Neil s question was as follows Now here is a foundational question for logicians on this list Is there any proof of existence of nonstandard models http://cs.nyu.edu/pipermail/fom/1997-December/000429.html

FOM: non-standard models, completeness, compactness Stephen G Simpson simpson at math.psu.edu Sat Dec 6 12:50:01 EST 1997 Previous message: FOM: Steve Simpson on K"onig's lemma, non-standard models etc. Next message: FOM: truth, meaning, undecidability: Steel, Shipman, Franzen Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: Steve Simpson on K"onig's lemma, non-standard models etc. Next message: FOM: truth, meaning, undecidability: Steel, Shipman, Franzen Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

29. 12. Non-standard Models 12. Nonstandard models. Non-standard models. From at least 1920 Skolem was sceptical of the use of predicate logic in characterizing mathematically http://www.hf.uio.no/ifikk/filosofi/njpl/vol1no2/pioneer/node12.html

Next: 13. Conclusion Up: Thoralf Skolem: Pioneer of Previous: 11. Elementary functions 12. Non-standard models From at least 1920 Skolem was sceptical of the use of predicate logic in characterizing mathematically useful structures. In he considered what he called set theoretic relativity. That is, the impossibilty of characterizing set theory in first-order logic. At that time he also seemed to have some thoughts about number theory. In he was more concrete. He considered the structure of polynomials in a variable x . We get a structure not too unlike the natural numbers themselves. We can for example order them by He was unable to get a structure elementary equivalent to number theory at once. He had to do some more work. In a number of papers we are able to see progressuntil . There he proved that it was impossible to characterize number theory with axioms from first-order logic. For the result he had to assume an enumeration of all statements. Now the proof may be given using ultraproducts. The assumption about an enumeration would then correspond to the existence of an ultrafilter. Skolem's result follows of course from Gödel's incompleteness result. But Skolem's result and technique is of independent interest. Nordic Journal of Philosophical Logic, Vol. 1, No. 2, pp. 107117.

30. Morphological Studies Of The CMB: Non-standard Models And Foregrounds - Digitale Jaffe, Theresa (2006) Morphological Studies of the CMB Nonstandard models and Foregrounds Dissertation, LMU München Fakultät für Physik http://edoc.ub.uni-muenchen.de/5950/

@import url(http://edoc.ub.uni-muenchen.de/style/auto.css); @import url(http://edoc.ub.uni-muenchen.de/style/print.css); Suche: Home Bl¤ttern Suchen Hilfe ... Registrieren Jaffe, Theresa Morphological Studies of the CMB: Non-standard Models and Foregrounds Dissertation, LMU M¼nchen: Fakult¤t f¼r Physik Vorschau PDF - Klicken Sie auf das PDF-Icon, um die Dissertation im Volltext herunterzuladen. Abstract Dokumententyp: Hochschulschrift (Dissertation, LMU M¼nchen) Keywords: cosmology, cosmic microwave background Dewey-Dezimalklassifikation: 500 Naturwissenschaften und Mathematik Fakult¤ten: Fakult¤t f¼r Physik Sprache der Hochschulschrift: Englisch Datum der m¼ndlichen Pr¼fung: 09 Oktober 2006 1. Gutachter/in: White, Simon URN des Dokumentes: urn:nbn:de:bvb:19-59503 MD5 Pr¼fsumme der PDF-Datei: Signatur der gedruckten Ausgabe: 0001/UMC 15716 ID: Hochgeladen von: Theresa Jaffe Hochgeladen am: 30. Oktober 2006 Zuletzt ge¤ndert: 06. November 2007 20:58 Nur f¼r Administratoren und Editoren: Dokument bearbeiten Dieser Server f¼r digitale Dissertationen der LMU verwendet EPrints 3,

31. Lumpy Pea Coat: Non-standard Models Of Arithmetic The first proofs of nonstandard models of arithmetic are due to Skolem in 1933 and 1934 but the connection could have been made earlier by the following http://nortexoid.blogspot.com/2005/06/non-standard-models-of-arithmetic.html

Lumpy Pea Coat Logic and Mannequins Thursday, June 09, 2005 Non-standard models of arithmetic But Kleene pointed out that G¶del's original proof of the incompleteness theorem was for Principia Mathematica which does not have the same form as FOL + PA axioms. So such a connection may not have been immediately evident until 1931-32 when G¶del generalized his theorem to arithmetical theories based on a familiar first-order calculus. On a related note, an interesting paper by Eklund, On How Logic Became First-order , argues against the Moore and Shapiro account that the move to first-order axiomatizations of arithmetic is due to Skolem and G¶del. Posted by lumpy pea coat at 10:36 AM 1 comments: us government grants said... UNBELIEVABLE....Do you know or have you ever heard of Gotting Money from us government grants ..If you are interested in finding out how to get more info on us government grants visit us at http://allgrants4u.com... There are so many things you can get grants for.. Homes, school, work, business, college..ect.. Find out how everybody is getting money from us government grants today... Quit living in poverty educate yourself and improve your life..

32. Non Standard Models Of PA It s well know that there exist no nonstandard models of PA for which . some non-standard model of PA. But is there an a priori reason why these http://www.groupsrv.com/science/about291930.html

Main Page Report this Page Enter your search terms Submit search form Web GroupSrv.com Loading.. Science Forum Index Logic Forum Page of Goto page Next Author Message Herman Jurjus Posted: Mon Oct 22, 2007 2:53 am Guest Hi all, It's well know that there exist no non-standard models of PA for which addition and/or multiplication are recursive. But is it also known whether such models exist for which addition and multiplication are PA-definable, or even just ZFC-definable? Cheers, Herman Jurjus Back to top Rupert Posted: Mon Oct 22, 2007 3:26 am Guest Quote: Hi all, It's well know that there exist no non-standard models of PA for which addition and/or multiplication are recursive. But is it also known whether such models exist for which addition and multiplication are PA-definable, or even just ZFC-definable? Cheers, Herman Jurjus Every arithmetically definable theory has a delta-1,1-definable model, the proof of the completeness theorem shows this. However, I don't know whether a nonstandard model of PA can be arithmetically definable. Back to top LauLuna Posted: Mon Oct 22, 2007 8:45 am

33. Edge: ON THE NATURE OF MATHEMATICAL CONCEPTS - By Verena Huber-Dyson [page 5] The existence of non standard models should NOT be confounded with the occurrence of incomplete concepts like that of a geometry or that of a set. http://www.edge.org/3rd_culture/huberdyson/huberdyson_p5.html

Home Third Culture Digerati Reality Club NON STANDARD MODELS In amazing contrast to TN the first order theory TR of the ordered field of the REALS has been successfully and completely formalized ÷ starting with Euclid's axioms, improved by Hilbert just before the turn of the century and completed as well as proved complete by Tarski about the time of the Second World War. My immediate reaction when I first heard of this feat was shock and distrust of those Berkeley logicians. "How could that be? The reals are so much more complicated than the integers. Aren't the natural numbers defined as the non negative integral reals?" Well, the solution of that conundrum lies in the LIMITATION OF EXPRESSIVE POWER INHERENT IN FORMAL LANGUAGES. As a matter of fact, the natural numbers are not "elementarily definable" among the reals; there is no wff of the language of R that picks out the natural numbers among the reals. What really lies at the basis of non standard objects like hyper reals is ÷ again ÷ the limitation inherent in first order languages. In the elementary language of real number theory we cannot distinguish between Archimedean and non Archimedean orderings and that opens the door to constructions that were scorned by my teachers although they might use infinitesimals as a handy figure of speech the way we still talk Platonically. We thought that Cauchy and Weierstrass' arithmetization of analysis had done away with that alleged abuse of language, but now it is back en vogue again and very useful too (see below).

34. Non Standard Models Of PA - Sci.logic | Google Groups If we have two models of ZFC, then in both models, our formulas lead to some nonstandard model of PA. But is there an a priori reason why these http://groups.google.nu/group/sci.logic/msg/4abc4380a7553a1a

Help Sign in sci.logic Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Non standard models of PA The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful Herman Jurjus View profile More options Oct 23, 7:19 pm Newsgroups: sci.logic From: Date: Wed, 24 Oct 2007 08:19:13 +0200 Local: Tues, Oct 23 2007 7:19 pm Subject: Re: Non standard models of PA Reply to author Forward Print View thread ... Find messages by this author Bill Taylor wrote: > ** there is no known "easily" defined nonstandard model of PA. It seems to me that such explicit formulas do exist, only they are probably very long. (What i have in mind is making a Henkin construction, but with 'fixed' enumeration of sentences, indexes of spare-constants, etc. in some explicit way. Dividing out the equivalence relation at the end is handled by identifying every equivalence class with its smallest member.)

35. Neutrino Heating In Non-Standard Models Of Big Bang Nucleosynthesis LC18.02 Neutrino Heating in NonStandard models of Big Bang Nucleosynthesis. Juan Lara (Center for Relativity, University of Texas at Austin) http://flux.aps.org/meetings/YR99/CENT99/abs/S4255002.html

Previous abstract Graphical version Next abstract Session LC18 - General Theory. FOCUS session, Tuesday afternoon, March 23 Room 258W, GWCC Neutrino Heating in Non-Standard Models of Big Bang Nucleosynthesis Juan Lara (Center for Relativity, University of Texas at Austin) Part L of program listing

36. SFU Institutional Repository: Item 1892/1805 In Chapter Two, we look at nonstandard models of topological groups and give the characterizations of some standard properties in non-standard terms. http://ir.lib.sfu.ca/handle/1892/1805

SFU.CA Burnaby Surrey Vancouver ... Z SFU Search Search DSpace: Advanced Search Home Browse Communities Titles Authors By Date Sign on Receive email updates My DSpace authorized users Edit Profile Info Help About The SFU Institutional Repository ... First Forty Theses Please use this identifier to cite or link to this item: http://hdl.handle.net/1892/1805 Title: An application of non-standard model theoretic methods to topological groups and infinite Galois theory. Authors: McKeever, Robert. Issue Date: Abstract: The purpose of this paper is to review some of the work done by Abraham Robinson in topological groups and infinite Galois Theory using ultrapowers as our method of obtaining non-standard models. Chapter One contains the basic logical foundations needed for the study of Non-Standard Analysis by the method of constructing ultrapowers. In Chapter Two, we look at non-standard models of topological groups and give the characterizations of some standard properties in non-standard terms. We also investigate a non-standard property that has no direct standard counterpart. In Chapter Three, we analyze an infinite field extension of a given field r and arrive at the correspondence between the subfields of our infinite field that are extensions of r and the subgroups of the corresponding Galois group through the Krull topology by non-standard methods. Description: Thesis (M.Sc.) - Dept. of Mathematics - Simon Fraser University

37. Tennenbaum S Theorem It is easily stated as saying that there is no Nonstandard recursive model of Peano Arithmetic, and is an attractive and rightly oftenquoted result. http://web.mat.bham.ac.uk/R.W.Kaye/papers/tennenbaum/tennhistory

Tennenbaum's Theorem Some historical background The theorem known as Tennenbaum's Theorem was given by Stanley Tennenbaum in a paper at the April meeting in Monterey, California, 1959, and published as a one-page abstract in the Notices of the American Mathematical Society . It is easily stated as saying that there is no nonstandard recursive model of Peano Arithmetic, and is an attractive and rightly often-quoted result. This paper celebrates Tennenbaum's Theorem; we state the result fully and give a proof of it and other related results later. This introduction is in the main historical. The goals of the latter parts of this paper are: to set out the connections between Tennenbaum's Theorem for models of arithmetic and the G¶del–Rosser Theorem and recursively inseparable sets; and to investigate stronger versions of Tennenbaum's Theorem and their relationship to some diophantine problems in systems of arithmetic. Tennenbaum's theorem was discovered in a period of foundational studies, associated particularly with Mostowski, where it still seemed conceivable that useful independence results for arithmetic could be achieved by a hands-on approach to building nonstandard models of arithmetic. Mostowski's own aspirations for the programme are clearly set out in his address to the 8th Congress of Polish mathematicians in September 1953

38. Non Standard Models Of PA - Sci.logic | Google Groups From Nam D. Nguyen namducngu @shaw.ca . Date Sun, 04 Nov 2007 163826 GMT. Local Sun, Nov 4 2007 1238 pm. Subject Re Non standard models of PA http://groups.google.vg/group/sci.logic/msg/1a64a2f9017e7d2e

Help Sign in sci.logic Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Non standard models of PA The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful Nam D. Nguyen View profile More options Nov 4, 12:38 pm Newsgroups: sci.logic From: "Nam D. Nguyen" <namducngu Date: Sun, 04 Nov 2007 16:38:26 GMT Local: Sun, Nov 4 2007 12:38 pm Subject: Re: Non standard models of PA Reply Reply to author Forward Print ... Find messages by this author Aatu Koskensilta wrote: There have been times where "a proposed new idea is not just useless twaddle" and where specifics details were mentioned, and yet the "intellectual interests" were still at the "status-quo" level: and still seem to be so. It usually takes two to Tango! There were times they didn't pay attention too, even the ideas were demonstrated to be coherent!

39. OMGBBQ, A-! awesomerossum, did you study nonstandard models in your math/logic class? That was my favorite subject in number theory. If you are a platonist about http://www.top-law-schools.com/forums/viewtopic.php?p=358258

40. Function And Variable Index - R 导论 Getting help ^ Vector arithmetic abline Lowlevel plotting commands ace Some non-standard models add1 Updating fitted models http://www.biosino.org/pages/newhtm/r/schtml/Function-and-variable-index.html

: Concept index , Previous: The command-line editor , Up: Top Appendix D 函数和变量索引 Logical vectors Logical vectors Multiplication %o% ... Formulae for statistical models

41. The Implications Of Gödel's Theorem Nonstandard models of Peano Arithmetic (can be proved without recourse to The non-standard model of Peano Arithmetic starts off with a progression of http://users.ox.ac.uk/~jrlucas/Godel/goedhand.html

Talk given to the Sigma Club on February 26th, 1998 by Mr J.R. Lucas wff. no. m . . . . (A n n m is neither provable not disprovable in first-order Peano Arithmetic (granted that it is consistent) has the following consequences: 1.Some purely arithmetical questions are undecidable-some research programmes may be hopeless. [J.Paris and L.Harrington, ``A Mathematical Incompleteness in Peano Arithmetic'', in J.Barwise, ed., Handbook of Mathematical Logic , Amsterdam, 1977.] So may-be we always shall be ignorant of the answers to some mathematical questions; no doctrine of Assurance. 3. Church's Theorem 5. Quine wrong in thinking first-order logic is cat's whiskers. See under III for difference between Peano's fifth postulate in first- and in second-order logic: Either we have only first-order logic, in which case we need some platonic access to the natural numbers in order to distinguish them from non-standard models of Peano Arithmetic: or we have second-order logic, which involves quantifcation over qualities and relations, which must then, Quinely, be supposed to exist. 6. Verificationism and Intuitionism are wrong.

42. Robinson (print-only) Proper extensions of noncomplete theories are often referred to as nonstandard models. A non-standard model for the system of real numbers has the feature http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Robinson.html

Abraham Robinson Born: 6 Oct 1918 in Waldenburg, Germany (now Walbrzych, Poland) Died: 11 April 1974 in New Haven, Connecticut, USA We should note at the outset that in fact Abraham Robinson 's family name was Robinsohn rather than Robinson, but we shall refer throughout this article to Robinson, the version which he used after 1940. Abraham Robinson's father was also named Abraham Robinson and his mother was Hedwig Lotte. He was the second child of the family, his older brother Saul Robinson also went on to have an outstanding career; he became an expert on comparative education. Abraham Robinson senior was also a highly talented man. After studying chemistry he became an important writer and philosopher but Abraham junior never knew his father for he died shortly before Abraham junior was born. It was a Jewish family and although Abraham Robinson senior was a Zionist he had never been to Palestine but he had accepted the position of head of the Hebrew National Library in Jerusalem just before he died. Hedwig Robinson was a teacher and she brought up her two sons in Germany until 1933 when Abraham was fourteen years old. Although little is known of Abraham during these years, some notebooks which he owned have survived [18]:- ... containing poems and plays, suggesting a sensitive observant child with an ambition to write.

43. "SH11B" In Fm99 Nevertheless, many nonstandard models have been proposed to explain, for example, the solar neutrino problem, the solar lithium depletion, and the faint http://www.agu.org/cgi-bin/wais?l=SH11B

44. Non-standard Model - Wikipedia, The Free Encyclopedia In model theory, a discipline within mathematical logic, a nonstandard model is a model of a theory that is not isomorphic to the intended model (or http://en.wikipedia.org/wiki/Non-standard_model

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Non-standard model From Wikipedia, the free encyclopedia Jump to: navigation search In model theory , a discipline within mathematical logic , a non-standard model is a model of a theory that is not isomorphic to the intended model (or standard model). If the intended model is infinite and the language is first-order , then the L¶wenheim-Skolem theorems guarantee the existence of non-standard models. The non-standard models can be chosen as elementary extensions or elementary substructures of the intended model. Non-standard models are studied in set theory non-standard analysis , and non-standard arithmetic This mathematical logic -related article is a stub . You can help Wikipedia by expanding it Retrieved from " http://en.wikipedia.org/wiki/Non-standard_model Categories Mathematical logic stubs Model theory Views Article Discussion Edit this page History Personal tools Sign in / create account Navigation Main Page Contents Featured content Current events ... Random article interaction About Wikipedia Community portal Recent changes Contact Wikipedia ... Help Search Toolbox What links here Related changes Upload file Special pages ... Cite this article Languages Fran§ais This page was last modified 21:22, 26 November 2007.

45. Phys. Rev. D 44 (1991): Robert Garisto And Gordon Kane - Non-standard-model CP . VOLUME 44, NUMBER 7 Nonstandard-model CP violation in K,,3 decays as a method of probing for new physics Robert Garisto and Gordon Kane Department of http://link.aps.org/doi/10.1103/PhysRevD.44.2038

Physical Review Online Archive Physical Review Online Archive AMERICAN PHYSICAL SOCIETY Home Browse Search Members ... Help Abstract/title Author: Full Record: Full Text: Title: Abstract: Cited Author: Collaboration: Affiliation: PACS: Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST PER Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article: MyArticles: View Collection Help (Click on the to add an article.) Phys. Rev. D 44, 2038 - 2049 (1991) Previous article Next article Issue 7 View Page Images PDF (1683 kB), or Buy this Article Use Article Pack Export Citation: BibTeX EndNote (RIS) Non-standard-model CP violation in K decays as a method of probing for new physics Robert Garisto and Gordon Kane Department of Physics, University of Michigan, Ann Arbor, Michigan 48109 Received 15 April 1991 The transverse polarization of the muon ( P ) in the decay K is a very useful tool for studying CP violation because a detectable nonzero P can only arise from physics beyond the standard model. Further, P is interesting because it probes a different region of parameter space than many other CP -violating observables. To help justify an experimental search, we present three models which give

46. Press Pass - Press Releases Searches for nonStandard Model Higgs bosons and exotic particles, presented by Ulrich Heintz, Boston University. Scientists think that dark matter is made http://www.fnal.gov/pub/presspass/press_releases/tevatronresults.html

April 15, 2007 Media Contact: At the APS conference, Jacksonville, Florida: David Harris, 650-704-0738 At Fermilab, Batavia, Illinois: Kurt Riesselmann, 630-531-8071 For immediate release Tevatron collider yields new results on subatomic matter, forces Batavia, IllinoisScientists of the CDF and DZero experiments at the Department of Energy's Fermi National Accelerator Laboratory presented today (April 15) at the annual April meeting of the American Physical Society the latest results of intriguing measurements made with the Tevatron particle collider. Highlights of the presentations were the observation of rare particle processes never observed before and new constraints on the mass of the Higgs boson, which in principle make the observation of this elusive particle at the Fermilab Tevatron collider more likely. Based on the world's best measurements of the top quark mass and the W boson mass, the new upper limit for the mass of the Higgs boson is now 144 GeV/c with 95 percent probability. More than 60 scientists working on the Tevatron experiments are presenting results at the APS meeting in Jacksonville, Florida. They are showing results for the rare production of single top quarks, one of the rarest collision processes ever observed at a hadron collider; a new measurement of the top quark mass; the first observation of events that simultaneously produce a W boson and a Z boson, an important milestone in the search for the Higgs boson; an update on measurements of bottom quarks, including B

47. Computational Complexity: A Non-Standard Post Now suppose P=NP in the standard model but P NP in some nonstandard model (and thus the P versus NP question is independent of the theory of arithmetic). http://weblog.fortnow.com/2005/03/non-standard-post.html

@import url("http://www.blogger.com/css/blog_controls.css"); @import url("http://www.blogger.com/dyn-css/authorization.css?blogID=3722233"); var BL_backlinkURL = "http://www.blogger.com/dyn-js/backlink_count.js";var BL_blogId = "3722233"; Computational Complexity About Computational complexity and other fun stuff in math and computer science as viewed by Bill Gasarch. Blog created and written until March 2007 by Lance Fortnow. My Links Bill's Home Page Lance's Home Page Weblog Home Weblog Archives and Search ... Favorite Theorems Recent Posts Getting an Edge My Brother P=NP and the Arts Complexity LaTeX Package ... The Reality of Virtual Pets Complexity Links IEEE Conference on Computational Complexity Electronic Colloquium on Computational Complexity BEATCS Computational Complexity Column Complexity Zoo ... Favorite Complexity Books Weblogs Andy Drucker Ars Mathematica Computing Research Policy D. Sivakumar ... Terence Tao Other Links DMANET FYI Nielsen's Principles of Research Parberry's TCS Guides ... Theorynet Discussion Groups Computer Science Theory Theory Edge This work is licensed under a Creative Commons License Tuesday, March 29, 2005

48. The Göbbellian Syndrome Further, the above argument would hold for every model of PA*, since the induction axiom of PA would hold in a nonstandard model (cf. http://alixcomsi.com/The Goebbellian Syndrome.htm

Index Main essay The Göbbellian Syndrome Can we really falsify truth by dictat? Bhupinder Singh Anand A .pdf file of this essay before the current update is available at http://arXiv.org/abs/math/0507046 1. Introduction – Non-standard models of PA In a 1996 talk on the Gödelian argument [Lu96], J. R. Lucas commented as follows:  in the case of First-order Peano Arithmetic there are Gödelian formulae (many, in fact infinitely many, one for each system of coding) which are not assigned truth-values by the rules of the system, and which could therefore be assigned either TRUE or FALSE, each such assignment yielding a logically possible, consistent system. These systems are random vaunts, all satisfying the core description of Peano Arithmetic. 2. A Göbbellian dictat? Can we really falsify truth by such a Göbbellian dictat? In other words, if [(A x R x )] is the PA-unprovable Gödelian formula - which is true under the standard interpretation - can we add its negation, [~(A x R x )], as an axiom to PA, and still obtain a consistent system? In his seminal 1931 paper, Gödel argued ([

49. Model Selection However, since we have chosen a nonstandard model, StyleADVISOR has given a reward for dropping one index, namely the Russell 1000 Value index. http://www.styleadvisor.com/support/statistics/model_selection.html

Style ADVISOR Online Support Session Frequently Asked Questions StyleADVISOR Statistics AllocationADVISOR Statistics ... Quick Tip Videos Model Selection The Advanced Parameters tab in the Edit Analysis Parameters dialog allows the user to set a number of parameters that modify the way the calculations are made. StyleADVISOR allows the user to modify the mathematical calculation used to analyze a manager's style. This is done on the Advanced Parameter tab in the Edit Analysis Parameters dialog under Model Selection. Changing the model will affect all style weights and style bases, i.e., it will affect the Manager Style and Asset Allocation graphs, as well as everything that involves a Style Benchmark. When the Standard Model is chosen, StyleADVISOR will perform the classical style analysis as set forth by William F. Sharpe. This means that StyleADVISOR will determine the style weights (i.e., the asset allocation) so as to minimize the variance of excess return. Looking at the formula for the standard R2 as explained earlier, it is easy to see that minimizing the variance of excess return is equivalent to maximizing the standard R2. The four other models all have one thing in common: They modify the calculation of the style weights so that there is a penalty for having a larger number of non-zero weights. In other words, there is a reward for dropping indices from the analysis.