Geometry.net Online Store

1. Infinite Ink: Cardinal Numbers Large cardinals are cardinals whose existence cannot be proved in ZFC. Examples include weakly inaccessible cardinals and inaccessible cardinals. http://www.ii.com/math/cardinals/

Trapped in a frame? Break free now! C ARDINAL N UMBERS A cardinal number is one way to measure the size of a set. Here is the definition used in Zermelo Fraenkel set theory (ZF): The cardinal (or cardinality ) of x, denoted card(x), is: the least ordinal a equinumerous to x, if x is well-orderable, and the set of all sets y of least rank which are equinumerous to x, otherwise. In ZFC all sets are well-orderable and only definition (1) above is needed. The purpose of this page is to describe the different types of cardinal numbers. For an introduction to cardinal and ordinal numbers see the ``Mathematics of CH'' section in my Continuum Hypothesis article Notation k l a is used for the Greek letter alpha and represents an ordinal; w is used for the Greek letter omega; aleph is used for the Hebrew letter aleph; and: aleph is used for aleph-zero, the zero'th well-ordered infinite cardinal; aleph w aleph w w w w w w x w aleph a is used for aleph-alpha, the alpha'th (or a 'th) well-ordered infinite cardinal. Since all well-ordered cardinals are ordinals, sometimes I use ordinal notation for a cardinal or vice versa. For example, when I say k aleph k , the k on the left is being used as a cardinal and the k on the right is being used as an ordinal.

2. Antimeta Large Cardinals And Their Justifications I m told that Larger Large cardinal axioms state similar properties about the universe and guarantee that we can bring them down to models of a certain form http://www.ocf.berkeley.edu/~easwaran/blog/2005/12/large_cardinals_and_their_jus

3. Special Session On Large Cardinals In Set Theory Special Session on Large cardinals in Set Theory. American Mathematical Society Sectional Meeting, Miami University, Oxford, Ohio, March 1617, 2007 http://www.users.muohio.edu/larsonpb/oxfordsession.html

Special Session on Large Cardinals in Set Theory American Mathematical Society Sectional Meeting, Miami University, Oxford, Ohio, March 16-17, 2007 This special session is being organized by Paul Larson Justin Moore and Ernest Schimmerling . The following is a tentative schedule of talks. The official schedule is posted here Friday AM Andreas Blass (9:00) Sheila Miller Jennifer Brown Stefan Geschke Bart Kastermans Tim Carlson Friday PM James Cummings Bernhard Koenig Elizabeth Brown Todd Eisworth ... Justin Moore Saturday AM Slawomir Solecki Christian Rosendal John Clemens Saturday PM Teruyuki Yorioka Stuart Zoble Richard Ketchersid Steve Jackson

4. Set Theory (Stanford Encyclopedia Of Philosophy) Along with the theory of Large cardinals it is used to gauge the consistency Since the pioneering work of Ronald Jensen, Large Cardinal Theory has been http://plato.stanford.edu/entries/set-theory/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Set Theory First published Thu 11 Jul, 2002 1. The Essence of Set Theory 2. Origins of Set Theory 3. The Continuum Hypothesis 4. Axiomatic Set Theory ... Related Entries 1. The Essence of Set Theory The objects of study of Set Theory are sets . As sets are fundamental objects that can be used to define all other concepts in mathematics, they are not defined in terms of more fundamental concepts. Rather, sets are introduced either informally, and are understood as something self-evident, or, as is now standard in modern mathematics, axiomatically, and their properties are postulated by the appropriate formal axioms. The language of set theory is based on a single fundamental relation, called membership . We say that A is a member of B (in symbols A B ), or that the set B contains A as its element. The understanding is that a set is determined by its elements; in other words, two sets are deemed equal if they have exactly the same elements. In practice, one considers sets of numbers, sets of points, sets of functions, sets of some other sets and so on. In theory, it is not necessary to distinguish between objects that are members and objects that contain members the only objects one needs for the theory are sets. See the supplement Basic Set Theory for further discussion.

5. Large Cardinals And Topology A Short Retrospective And Some New The author s purpose is to present some applications of Large cardinals in general topology, pointing out that there are several topological problems that http://jigpal.oxfordjournals.org/cgi/content/abstract/15/5-6/433

6. JSTOR The Higher Infinite. Large Cardinals In Set Theory From This book is now the main reference for the theory of Large cardinals in set theory. The material in it is well organized and is presented very clearly. http://links.jstor.org/sici?sici=0022-4812(199603)61:1<334:THILCI>2.0.CO;2-2

7. 288:Discrete Ordered Rings And Large Cardinals REQUIRING AN EXTREME Large CARDINAL. Let R be a discrete ordered ring. Let E containedin R^k. We say that V is a subpower of E if and only if V containedin http://osdir.com/ml/science.mathematics.fom/2006-06/msg00006.html

var addthis_pub = 'comforteagle'; science.mathematics.fom Top All Lists Date Thread 288:Discrete ordered rings and large cardinals Subject 288:Discrete ordered rings and large cardinals List-id We first correct a typo in #287, http://www.cs.nyu.edu/pipermail/fom/2006-May/010568.html http://www.cs.nyu.edu/pipermail/fom/2006-May/010505.html http://www.math.ohio-state.edu/%7Efriedman/ for downloadable manuscripts. This is the 288th in a series of self contained numbered postings to FOM covering a wide range of topics in f.o.m. The list of previous numbered postings #1-249 can be found at http://www.cs.nyu.edu/pipermail/fom/2005-June/008999.html More with this subject... Current Thread Previous by Date: Re: explicit variables William Tait Next by Date: Re: Quantum mechanics solved(?) scerir Previous by Thread: Re: explicit variables William Tait Next by Thread: Re: Algebraic closure of Q Stephen G Simpson Indexes: Date Thread Top All Lists Recently Viewed: qnx.openqnx.dev... network.tin.bug... hardware.sony.l... text.xml.cocoon... ... advertise var dc_UnitID = 14; var dc_PublisherID = 4576; var dc_AdLinkColor = 'blue'; var dc_adprod='ADL';

8. [math/9811187] Finite Functions And The Necessary Use Of Large Cardinals The proofs of these theorems illustrate in clear terms how one uses the well studied higher infinities of abstract set theory called Large cardinals in an http://arxiv.org/abs/math.LO/9811187

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: Finite functions and the necessary use of large cardinals Authors: Harvey M. Friedman (Submitted on 1 Nov 1998) Abstract: We present a coherent collection of finite mathematical theorems some of which can only be proved by going well beyond the usual axioms for mathematics. The proofs of these theorems illustrate in clear terms how one uses the well studied higher infinities of abstract set theory called large cardinals in an essential way in order to derive results in the context of the natural numbers. The findings raise the specific issue of what consitutes a valid mathematical proof and the general issue of objectivity in mathematics in a down to earth way. Large cardinal axioms, which go beyond the usual axioms for mathematics, have been commonly used in abstract set theory since the 1960's. We believe that the results reported on here are the early stages of an evolutionary process in which new axioms for mathematics will be commonly used in an essential way in the more concrete parts of mathematics. Comments: 91 pages, published version

9. A Universal Extender Model Without Large Cardinals In V We construct, assuming that there is no inner model with a Woodin cardinal but without any Large cardinal assumption, a model Kc which is iterable for set http://projecteuclid.org/handle/euclid.jsl/1082418531

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next A universal extender model without large cardinals in V William Mitchell and Ralf Schindler Source: J. Symbolic Logic Volume 69, Issue 2 (2004), 371-386. Abstract We construct, assuming that there is no inner model with a Woodin cardinal but without any large cardinal assumption, a model K c which is iterable for set length iterations, which is universal with respect to all weasels with which it can be compared, and (assuming GCH) is universal with respect to set sized premice. Primary Subjects: Keywords: Set theory; core models; large cardinals Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.jsl/1082418531

10. Books - Inner Models And Large Cardinals - 9783110163681 Buy Inner Models and Large cardinals Price Range $80.50 - $154.74 from 4 sellers. http://www.pricegrabber.com/search_getprod.php/isbn=9783110163681

Go back to home page Login Register Your Lists ... Holiday Guide SHOP FOR IN All Products Appliances Auto Parts Books Cameras Clothing Computers Electronics Furniture Indoor Living Magazines Movies Music Musical Instruments Office Outdoor Living Software Sporting Goods Toys Video Games SEARCH Sell Yours Save Product to Your List(s) (Javascript required) Set Price Alert Inner Models and Large Cardinals (English) (ISBN: 9783110163681) Price range: $80.50 (Refurb) - $154.74 from 4 Sellers Publisher: Walter De Gruyter Inc Format: Hardcover MSRP: $ 128.95 Synopsis: Not Available User Reviews Not Rated Write a Review Compare Prices Book Details New (1 Seller for $80.50) View All Conditions Enter Zip Code* Seller Price (USD) Tax* Shipping* BottomLinePrice* Availability Seller Rating Amazon.com Merchant Info No Tax Free Your Best Price In Stock 355 Reviews Alibris Merchant Info No Tax In Stock 354 Reviews Amazon.com Marketplace Merchant Info No Tax See Site See Site In Stock Fewer than 10 reviews Enter Zip Code* * Enter your zip code above to get the best price for delivery in your area including shipping and tax. Shipping costs are based on an estimate of UPS ground or equivalent carrier within the contiguous US, excluding Alaska and Hawaii. Please see Seller's website for actual shipping costs.

11. Logic Seminars 1998-98 Large cardinals III compactness; elementary embeddings. February 18, 1999 Large cardinals V elementary embeddings; indescribability. March 9, 1999 http://www.math.cornell.edu/~shore/sem989.html

Logic Seminars September 3, 1998 John Rosenthal, Ithaca College Finite dimensional Steinitz exchange systems with undecidable September 8, 1998 Joe Miller, Cornell University Forgetful determinacy September 10, 1998 Richard Platek, Cornell University Nonstandard analysis, an introduction September 15, 1998 Joe Miller, Cornell University The decidability of S2S via determinacy September 17, 1998 Richard Platek, Cornell University Nonstandard analysis II September 22, 1998 Suman Ganguli, Cornell University The decidability of S2S via determinacy September 24, 1998 Richard Platek, Cornell University Nonstandard analysis III September 29, 1998 The decidability of S2S via determinacy, continued October 1, 1998 Robert Milnikel, Cornell University Reduction of nonstandard mathematics to standard October 8, 1998 Moshe Vardi, Rice University Church's problem revisited: synthesis with incomplete information and alternating tree automata October 15, 1998 Walker White, Cornell University Radically finite probability theory October 22, 1998

12. Atlas: Weak Squares, And Large Cardinals Between Superstrong And Supercompact By Most of these principles are known to be false/consistently false retaltive to a supercompact cardinal. I will introduce Large cardinal axioms which can http://atlas-conferences.com/c/a/i/r/04.htm

Atlas home Conferences Abstracts about Atlas Boise Extravaganza In Set Theory March 29-31, 2002 Boise State University Boise, ID, USA Organizers Tomek Bartoszynski, Paul Corazza, Justin Moore View Abstracts Conference Homepage Weak squares, and large cardinals between superstrong and supercompact by Martin Zeman University of California, Irvine I will discuss various weak versions of the square principle. Most of these principles are known to be false/consistently false retaltive to a supercompact cardinal. I will introduce large cardinal axioms which can still prove the failure of weak square principles and which are candidates for optimal hypotheses for this task. Date received: March 11, 2002 Atlas Conferences Inc. Document # cair-04.

13. IngentaConnect Filters And Large Cardinals Filters and Large cardinals. Author Levinski J.P.1. Source Annals of Pure and Applied Logic, Volume 72, Number 2, 31 March 1995 , pp. 177-212(36) http://www.ingentaconnect.com/content/els/01680072/1995/00000072/00000002/art000

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Filters and large cardinals Author: Levinski J.-P. Source: Annals of Pure and Applied Logic , Volume 72, Number 2, 31 March 1995 , pp. 177-212(36) Publisher: Elsevier view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Language: English Document Type: Research article DOI: 10.1016/0168-0072(94)00015-U Affiliations: Departement de Mathematiques, Universite de Caen, 14032 Caen, France

14. Categories: Topos Theory And Large Cardinals One answer is Grothendieck universes , but they correspond to rather small Large cardinals. Can we go further than that? Andrej Bauer School of Computer http://north.ecc.edu/alsani/ct99-00(8-12)/msg00117.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index categories: Topos theory and large cardinals To categories@mta.ca Subject : categories: Topos theory and large cardinals From Andrej.Bauer@cs.cmu.edu Date : 01 Mar 2000 22:29:58 -0500 Sender cat-dist@mta.ca Source-Info : Sender is really andrej+@gs2.sp.cs.cmu.edu User-Agent : Gnus/5.0803 (Gnus v5.8.3) XEmacs/20.4 (Emerald) Can you complete this analogy? ``Large cardinals are to ZFC, as are to topos theory.'' One answer is "Grothendieck universes", but they correspond to rather small large cardinals. Can we go further than that? Andrej Bauer School of Computer Science Carnegie Mellon University http://andrej.com Prev by Date: categories: Johnstone review of Clark/Davey Next by Date: categories: dom fibration Prev by thread: categories: Johnstone review of Clark/Davey Next by thread: categories: Topos theory and large cardinals Index(es): Date Thread

15. Alex Hellsten: Diamonds On Large Cardinals Diamonds on Large cardinals. Alex Hellsten. Academic Dissertation, December 2003. University of Helsinki, Faculty of Science, Department of Mathematics http://ethesis.helsinki.fi/julkaisut/mat/matem/vk/hellsten/

University of Helsinki, Helsinki 2003 Diamonds on large cardinals Alex Hellsten Academic Dissertation, December 2003. University of Helsinki, Faculty of Science, Department of Mathematics As a PDF file (ISBN 952-10-1502-0) - 94 kb

16. Award#0556223 - Large Cardinals The PI is investigating the theory of Large cardinals, and their applications to determinacy, with emphasis on the following http://www.checkout.org.cn/awardsearch/showAward.do?AwardNumber=0556223

17. Von Neumann's Problem And Large Cardinals -- Farah And Velickovic 38 (6): 907 -- We use some ideas of Gitik and Shelah and implications from the inner model theory to show that some Large cardinal assumptions are necessary for this http://blms.oxfordjournals.org/cgi/content/abstract/38/6/907

@import "/resource/css/hw.css"; @import "/resource/css/blms.css"; Skip Navigation Oxford Journals Contact Us My Basket ... Volume 38, Number 6 Pp. 907-912 Previous Article Next Article Bulletin of the London Mathematical Society 2006 38(6):907-912; doi:10.1112/S0024609306018704 This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive ... Request Permissions Google Scholar Articles by Farah, I. Articles by Velickovic, B. Search for Related Content Von Neumann's Problem and Large Cardinals Ilijas Farah and Boban Veli kovi Department of Mathematics and Statistics, York University 4700 Keele Street, North York, Ontario, Canada, M3J 1P3 and Matematicki Institut Kneza Mihaila 35, Beograd, Serbia and Montenegro e-mail: Received 31 January 2005. Revision received 17 August 2005. It is a well-known problem of Von Neumann to discover whether the countable chain condition and weak distributivity of a complete Boolean algebra imply that it carries a strictly positive probability and by Veli kovi , that it is consistent with ZFC, modulo the consistency of a supercompact cardinal, that every ccc weakly

18. The Higher Infinite - Mathematische Logik Und Mengenlehre Journals, Books & Onli The theory of Large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative http://www.springer.com/dal/home/math?SGWID=1-10042-22-2312810-0

19. LARGE CARDINALS When considering these Large objects, we might also want to see if the notion of counting order coincides with that of cardinal defined above for these http://www.websters-online-dictionary.org/definition/LARGE CARDINALS

Philip M. Parker, INSEAD. LARGE CARDINALS Specialty Definition: Cardinal number (From Wikipedia , the free Encyclopedia) In mathematics, cardinal numbers , or cardinals for short, are numbers used to denote the size of a set. A natural number can be used for two purposes: to describe the size of a set, or to describe the position of an element in a sequence. While in the finite world these two concepts coincide, when dealing with infinite sets one has to distinguish between the two. This idea was developed by Georg Cantor. The position aspect leads to ordinal numbers, which were also discovered by Cantor, while the size aspect is generalized by the cardinal numbers described here. Two sets X and Y are said to have the same cardinality if there exists a bijection between X and Y X Y X itself is often defined as the least ordinal number a a X some ordinal; this statement is the well-ordering principle.) Motivation The intuitive idea of a cardinal is to create some notion of the relative size or "bigness" of a set without reference to the kind of members which it has. For finite sets this is easy; one simply counts the number of elements a set has. In order to compare the sizes of larger sets, its necessary to appeal to more subtle notions. A set Y is at least as big as a set X if there is a one-to-one mapping from the elements of X to the elements of Y . This is most easily understood by an example; suppose we have the sets

20. Interests Results for communities interested in Large cardinals . 1 match. info settheory Set Theory (Last updated 16 weeks ago) http://www.livejournal.com/interests.bml?int=large cardinals

21. CJO - Abstract - THE HIGHER INFINITE. LARGE CARDINALS IN SET THEORY FROM THEIR B Large cardinals IN SET THEORY FROM THEIR BEGINNINGS (Perspectives in Mathematical Logic) By Akihiro Kanamori 536 pp., DM. 178. http://journals.cambridge.org/abstract_S0024609396221678

By Akihiro Kanamori: 536 pp., DM.178.-, ISBN 3 540 57071 3 (Springer, 1994). CLASSICAL DESCRIPTIVE SET THEORY (Graduate Texts in Mathematics) By Alexander S. Kechris: 402 pp., DM.79.-, ISBN 387 94374 9 (Springer, 1995). @import url("/css/users_abstract.css"); close Cambridge Journals Online Skip to content Volume 29 Issue 01 - Jan 1997 Cited by Articles (Google Scholar) ... Bulletin of the London Mathematical Society (1997), 29: 109-127 Cambridge University Press *This article is available in a PDF that may contain more than one articles. Therefore the PDF file's first page may not match this article's first page. Login Subscribe to journal Email abstract Save article ... Link to this abstract Copy and paste this link: http://journals.cambridge.org/action/displayAbstract?aid=18911 Book Review THE HIGHER INFINITE. LARGE CARDINALS IN SET THEORY FROM THEIR BEGINNINGS (Perspectives in Mathematical Logic)

22. The Higher Infinite: Large Cardinals In Set Theory From Their Beginnings Price C Compare The Higher Infinite Large cardinals in Set Theory from Their Beginnings prices before you buy to make sure you get the best deal. http://shopping.msn.com/prices/shp/?itemId=1573700

23. DC MetaData For: Von Neumann's Problem And Large Cardinals MSC 03E55 Large cardinals 28A99 None of the above but in this section. Abstract It is a well known problem of Von Neumann whether the countable chain http://www.esi.ac.at/Preprint-shadows/esi1600.html

Ilijas Farah, Boban Velickovic Von Neumann's Problem and Large Cardinals Preprint series: ESI preprints MSC 03E55 Large cardinals 28A99 None of the above but in this section Abstract It is a well known problem of Von Neumann whether the countable chain condition and weak distributivity of a complete Boolean algebra imply that it carries a strictly positive probability measure. It was shown recently that it is consistent with ZFC, modulo the consistency of a supercompact cardinal, that every ccc weakly distributive complete Boolean algebra carries a contiuous strictly positive submeasure, i.e., is a Maharam algebra. We use some ideas of Gitik and Shelah to show that some large cardinal assumptions are necessary for this result.

24. Arthur W. Apter Some Results on Consecutive Large cardinals II Applications of Radin Forcing , Israel Journal of Mathematics 52, 1985, 273292. http://math.baruch.cuny.edu/~apter

Arthur W. Apter Professor of Mathematics Baruch College of CUNY Professor of Mathematics The CUNY Graduate Center Email address: awapter at alum dot mit dot edu Education: B.S., Mathematics M.I.T. Ph.D., Mathematics ... Joel Hamkins , whom I thank for helping me to set up this web page, has created a page containing links of interest to logicians both in the greater New York area and elsewhere. Click here here , or here to access these links. Click here to find out information about MAMLS. Slides: Slides from my lecture "Some Results Concerning Strong Compactness and Supercompactness", which I presented at the Winter Meeting of the ASL held January 17-18, 2003 in Baltimore, can be found by clicking here for the .dvi file, and here for the LaTeX file. Slides from my lecture "Indestructibility and Strong Compactness", which I presented at Logic Colloquium 2003 held August 14-20, 2003 in Helsinki, Finland can be found by clicking here for the .dvi file, and here for the LaTeX file. Slides from the lecture I presented at the Baumgartner 60th Birthday Conference, held October 4-5, 2003 at Dartmouth College can be found by clicking here for the .dvi file, and

25. Large Cardinal - Indopedia, The Indological Knowledgebase In mathematics, a cardinal is called a Large cardinal if it belongs to a class of cardinals, the existence of which provably cannot be proved within the http://www.indopedia.org/Large_cardinal.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS Categories Set theory Printable version Wikipedia Article Large cardinal ज्ञानकोश: - The Indological Knowledgebase In mathematics , a cardinal is called a large cardinal if it belongs to a class of cardinals, the existence of which provably cannot be proved within the standard axiomatic set theory ZFC , if one assumes ZFC itself is consistent. Therefore the discussion of large cardinals takes place in a realm of conditional proofs , which (according to the consensus view of logicians) will remain so. weakly inaccessible cardinals strongly inaccessible cardinals (actually the same consistency strength as weakly inaccessible) Mahlo cardinals n -Mahlo cardinals weakly compact cardinals m n indescribable cardinals totally indescribable cardinals unfoldable cardinals subtle cardinals ... remarkable cardinals (not a cardinal, but proves the existence of transitive models with the cardinals above) Almost Ramsey cardinals Ramsey cardinals measurable cardinals strong cardinals ... edit Other types of large cardinals unfoldable cardinals n -ineffable cardinals totally ineffable cardinals ... extendible cardinals Retrieved from " http://www.indopedia.org/Large_cardinal.html

26. Large Cardinals And Their Justifications « Antimeta I’m told that Larger Large cardinal axioms state similar properties about the universe and guarantee that we can bring them down to models of a certain form http://antimeta.wordpress.com/2005/12/05/large-cardinals-and-their-justification

Antimeta A general distrust of strong metaphysical claims in mathematics and philosophy. Home Large Cardinals and their Justifications Completeness theorem (which requires some fragment of ZFC to prove), we know that if Con(T) is the case, then there is actually some set and a collection of relations and functions on that set that can be used as the interpretation of the symbols in T to make it come out true. That is, any consistent theory (according to the numerical coding) has a model. Thus, if we think that ZFC+Con(ZFC) is a reasonable formulation of some part of mathematics, then there must in addition be some model of ZFC. If in addition, we assume Con(ZFC+Con(ZFC)), then there is a model of ZFC, which itself contains a model of ZFC. I , then there is in fact a set (called V I all their subsets, not just some of them), and thus has a lot more properties in common with the whole of mathematical reality than the other sorts of models of ZFC. In fact, it contains all the natural numbers and knows which set is the set of all natural numbers, so it knows any true statement (or true according to the fiction of mathematics, or whatever) of the form Con(T). So if there is an inaccessible cardinal, then V I is a model of ZFC, so Con(ZFC) is true, so

27. Large Cap - Definition Of Large Cap By The Free Online Dictionary, Thesaurus And Large cardinal hypotheses Large cardinal hypothesis Large cardinal property Large cardinal theory Large cardinals Large Cargo Freighter http://www.thefreedictionary.com/large cap

Domain='thefreedictionary.com' word='large cap' Printer Friendly 728,491,259 visitors served. TheFreeDictionary Google Word / Article Starts with Ends with Text subscription: Dictionary/ thesaurus Medical dictionary Legal dictionary Financial dictionary Acronyms Idioms Encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia large cap Also found in: Financial Wikipedia Hutchinson 0.03 sec. large cap adj. Of or relating to large corporations that have considerable retained earnings and a large amount of common stock outstanding. Of or relating to mutual funds that invest in the stock of such corporation. n. A large cap corporation. large cap Thesaurus Legend: Synonyms Related Words Antonyms Noun large cap - a corporation with a large capitalization; "he works for a large cap" corp corporation - a business firm whose articles of incorporation have been approved in some state Page tools Printer friendly Cite / link Email Feedback Add definition Charity('US') document.write('') Mentioned in References in classic literature corp corporation Entoloma Entoloma sinuatum ... Lepiota rhacodes In a sitting-room on the ground-floor, ensconced in an armchair with her back to the light, was the owner and mistress of the estate, a white-haired woman of not more than sixty, or even less, wearing a large cap Tess of the d'Urbervilles - A Pure Woman by Hardy, Thomas

28. Large Cardinals And Definable Well-Orderings Of The Universe Large cardinals and Definable WellOrderings of the Universe. Authors, Brooke-Taylor, Andrew D. Publication, eprint arXiv0711.2591. Publication Date http://adsabs.harvard.edu/abs/2007arXiv0711.2591B

Sign on Smithsonian/NASA ADS arXiv e-prints Abstract Service Find Similar Abstracts (with default settings below arXiv e-print (arXiv:0711.2591) Also-Read Articles Reads History Translate Abstract Title: Large Cardinals and Definable Well-Orderings of the Universe Authors: Publication: eprint arXiv:0711.2591 Publication Date: Origin: ARXIV Keywords: Mathematics - Logic, 03E35, 03E55, 03E25 Comment: 18 pages, submitted with Kurt Goedel Centenary Research Prize Fellowship application Bibliographic Code: Abstract We use a reverse Easton forcing iteration to obtain a universe with a definable well-ordering, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle diamond star at a proper class of successor cardinals. Bibtex entry for this abstract Preferred format for this abstract (see Preferences Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints Smithsonian/NASA ADS Homepage ADS Sitemap Query Form Basic Search ... FAQ

29. 14K Gold St Louis Cardinals Large Baseball Cap Charm 14K Gold St Louis cardinals Large Baseball Cap Charm Go cardinals! Official licensed MLB charm. This St Louis cardinals Charm comes in a lovely gift box, http://www.highperformancesportsjewelry.com/14kgostlocal1.html

home about us send email site map ... High Performance Sports Jewelry Toll Free 866-624-6180 Free Ground Shipping on any order! Search Home MLB Team Charms St. Louis Cardinals St. Louis Cardinals Charms 14K Gold St Louis Cardinals Large Baseball Cap Charm 14K Gold St Louis Cardinals Large Baseball Cap Charm-QG-ML1631 Item# QG-ML1631 Regular price: $153.00 Sale price: Availability: Usually ships in 2-3 business days. Product Description 14K Gold St Louis Cardinals Large Baseball Cap Charm Go Cardinals! Official licensed MLB charm. This St Louis Cardinals Charm comes in a lovely gift box, ready to be given as a gift. All gold jewelry weights are approximate. Free Ground Shipping on any order, use coupon code FreeShipping at Checkout Other Items in the Category: 14K Gold St Louis Cardinals X-Large Cardinals W/Bird Charm-QG-ML1635 14K Gold St Louis Cardinals Large Jersey Charm-QG-ML1628 Sterling Silver St Louis Cardinals Large Jersey Charm-QG-ML1628SS 14K Gold St Louis Cardinals Medium Jersey Charm-QG-ML1629 ... view cart // Begin Y! Store Generated Code

30. [0711.2591v1] Large Cardinals And Definable Well-Orderings Of The Universe Title Large cardinals and Definable WellOrderings of the Universe. Authors Andrew D. Brooke-Taylor. (Submitted on 16 Nov 2007) http://aps.arxiv.org/abs/0711.2591v1

aps.arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Full-text links: Download: PostScript PDF Other formats Citations CiteBase p revious n ... ext Mathematics > Logic Title: Large Cardinals and Definable Well-Orderings of the Universe Authors: Andrew D. Brooke-Taylor (Submitted on 16 Nov 2007) Abstract: We use a reverse Easton forcing iteration to obtain a universe with a definable well-ordering, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle diamond star at a proper class of successor cardinals. Comments: 18 pages, submitted with Kurt Goedel Centenary Research Prize Fellowship application Subjects: Logic (math.LO) MSC classes: Cite as: arXiv:0711.2591v1 [math.LO] Submission history From: Andrew Brooke-Taylor [ view email Fri, 16 Nov 2007 11:28:36 GMT (18kb) Which authors of this paper are endorsers? Link back to: arXiv form interface contact

31. Award#0094174 - CAREER: Large Cardinals The PI is investigating several aspects of Large cardinal theory in the iterable models for specific Large cardinals can be used to yield the http://nsf.gov/awardsearch/showAward.do?AwardNumber=0094174

32. Arbeitsgruppe Mathematische Logik | Main / Set Theory Browse The theory of ZFC; Large cardinals; Inner Models and Fine Structure Core model theory tries to realize Large cardinal axioms in canonical, http://www.mathematik.uni-muenchen.de/~logik/SetTheory

Arbeitsgruppe Mathematische Logik Aktuelles Kontakt Personen Forschung ... Studium Set Theory at the University of Munich People Prof. Dr. Hans-Dieter Donder Research Interests Inner Models and Fine Structure Infinite Combinatorics Equiconsistency Results Large Cardinals Set Theory was invented by Georg Cantor (1845 - 1918), and revolutionized mathematics. It's main theme is infinity. The research areas of modern set theory are: The theory of ZFC Large Cardinals Inner Models and Fine Structure Descriptive Set Theory Forcing Infinite Combinatorics Set Theory provides an universal framework in which all of mathematics can be interpreted. There is no competing theory in that respect. A well-known formulation of the basic set theoretic principles is given by the axiomatic system ZFC of Ernst Zermelo and Abraham Fraenkel, formalized in first order logic (the C denotes the axiom of choice). ZFC, however, does not decide the size of the reals: Cantor's Continuum Hypothesis (CH) is independent of ZFC (Goedel 1938, Cohen 1963). This result marks the beginning of modern Set Theory. Not only (CH) but many other propositions were shown to be independent. The methods used to prove independence are inner models - natural realizations of the axioms, the most prominent being Goedel's constructible universe L - and forcing - Cohen's method to enlarge given models of set theory keeping control of the new sets.

33. DOCUMENTA MATHEMATICA, Extra Vol. ICM II (1998), 11-21 Title Generic Large cardinals New Axioms for Mathematics? This article discusses various attempts at strengthening the axioms for mathematics, http://www.math.uiuc.edu/documenta/xvol-icm/01/Foreman.MAN.html

D OCUMENTA M ATHEMATICA , Extra Volume ICM II (1998), 11-21 Matthew Foreman Title: Generic Large Cardinals: New Axioms for Mathematics? 1991 Mathematics Subject Classification: Keywords and Phrases: axioms, large cardinals, ideals, generic large cardinals Full text: dvi.gz 21 k, dvi 48 k, ps.gz 63 k. Home Page of D OCUMENTA M ATHEMATICA

34. Sci.math FAQ: The Continuum Hypothesis Most Large cardinal axioms (asserting the existence of cardinals with various properties of hugeness these are usually derived either from considering the http://www.faqs.org/faqs/sci-math-faq/AC/ContinuumHyp/

Usenet FAQs Search Web FAQs Documents ... RFC Index sci.math FAQ: The Continuum Hypothesis Newsgroups: sci.math alopez-o@neumann.uwaterloo.ca alopez-o@barrow.uwaterloo.ca Tue Apr 04 17:26:57 EDT 1995 Rate this FAQ N/A Worst Weak OK Good Great Related questions and answers Usenet FAQs Search Web FAQs ... RFC Index Send corrections/additions to the FAQ Maintainer: alopez-o@neumann.uwaterloo.ca Last Update May 13 2007 @ 00:24 AM

35. Large Cardinals Large cardinals. In the mathematical theory of the infinite, classes of cardinals which are very remote have been considered, with names such as http://www.quadibloc.com/math/inf02.htm

Up Previous Mathematics Other ... Home Large Cardinals In the mathematical theory of the infinite, classes of cardinals which are very remote have been considered, with names such as inaccessible cardinals, strongly inaccessible cardinals, Mahlo cardinals, hyper-Mahlo cardinals, and so on. While I will not begin to attempt to touch on much of this here, I have encountered a way to provide a small taste of some of this. A few simple axioms suffice to define a set the number of whose elements must be a strongly inaccessible cardinal, unless it has either no elements or aleph-null elements. This kind of set is defined as a Grothendieck universe The axioms which define such a universe are: If any set is a member of that universe, then all of its elements are also members of that universe; The set whose members are any pair of elements of that universe is also an element of that universe; If a set is a member of that universe, then the set of those sets which include any combination of the members of that set, which is known as the power set of that original set, is also an element of that universe; For any set A which is a member of that universe, and for any set B of elements of that universe which are themselves sets and which can be placed in a one-to-one correspondence with the elements of set A, the union of all the sets which are elements of set B is also an element of that universe.

36. Papers.html The axioms are generalizations of Large cardinal axioms and their Assuming appropriate Large cardinals, it contains many results about when a new http://www.math.uci.edu/personnel/Foreman/homepage/newpapers.html

Annotated List of Matt Foreman's Papers: The papers below are organized by subject matter and annotated with comments. If you prefer a simple chronological listing go here. Click to jump to one of the Topics A.) Paradoxical decompositions and the Banach-Tarski Paradox with nice pieces B.) A descriptive view of ergodic theory C.) Amenable group actions, the Rusiewicz problem, the Hahn-Banach theorem and Lebesgue measurability. D.) Foundations of mathematics. E.) Consistency results of foundational interest F.) Model Theory: (Non-regular ultrafilters, Chang's Conjecture, Lowenheim-Skolem Theorems). G.) Saturated Ideals H.) Natural structure in set theory I.) Applications of set theory to Abelian groups and modules. J.) Aronzahn Trees K.) Hungarian Combinatorics L.) Pot Pouri A.) Paradoxical decompositions and the Banach-Tarski Paradox with nice pieces: The main result also gives paradoxical decompositions without the Axiom of Choice of open dense subsets of S^n. Banach-Tarski Decompositions Using Sets with the Property of Baire , (Joint with R. Dougherty.)

37. Amherst Magazine Spring 2007: Raising The Bar What are called “Large cardinals” are very Large sizes of infinity. Cotter’s thesis is about set theory, Large cardinals and a mathematical puzzle. http://www.amherst.edu/magazine/issues/07spring/raising_bar/index.html

Amherst Magazine Jump to main content. Amherst College Site Map Search ... Spring 2007 Raising the Bar By Emily Gold Boutilier Majors: History and physics Hometown: Palo Alto, Calif. Activities: Captain, Ultimate Frisbee team; cofounder, Sudan Divestment Project Immediate plan: Teach for America or U.S. State Department Critical Language Scholarship in Tajikistan Irwin is a history buff who speaks four foreign languages and has a knack for science. His thesis reconsiders a 1936 land reform project in the Laguna region of northern Mexico. The reform transformed much of the area into collective farms, known as ejidos . But by 1946, while private farms saw profits, half of the ejidos in the region had accumulated so much debt that the bank had cut off their lines of credit. Scholars have since deemed the reform a failure, blaming either population growth or the collective model itself. ejidos Major: Math Hometown: Babylon, N.Y. Activity: Orchestra manager Immediate Plan: Graduate school in math Working with adviser Jim Henle, a professor of mathematics at Smith College and an expert on large cardinals, Cotter studied and tied together the small, esoteric body of literature on the algebra solution. Her thesis is the first to explain, comprehensively, why the proof works.

38. RECERCAT (Diposit De La Recerca De Catalunya): Document 2072/1187 Title, Large cardinals and Llike universes. Autors, Friedman, Sy D. Altres autors, Centre de Recerca Matemàtica. Keywords, Nombres cardinals http://www.recercat.net/handle/2072/1187

Search Advanced Search What is it? Statistics News ... Castellano Please use this identifier to cite or link to this item: http://hdl.handle.net/2072/1187 Title: Large cardinals and L-like universes Autors: Friedman, Sy D. Altres autors: Centre de Recerca Matem tica Keywords: Nombres cardinals Publisher: Centre de Recerca Matem tica Collections: Prepublicacions del Centre de Recerca Matem tica;648 Appears in Collections: Prepublicacions del Centre de Recerca Matem tica Files in This Item: File Description Size Format Pr648.pdf Adobe PDF View/Open Recommend this item This item is licensed under a Creative Commons license Last Update: 01/02/07

39. Advogato: Blog For Bram I believe that the statement of the existence of Large cardinals is, in fact, concrete. Clearly they aren t conrete in the strict sense, http://www.advogato.org/person/Bram/diary.html?start=6

40. Sergio Fratarcangeli Logic Seminar Thursday, 29 September 2005 Rob Owen on Large cardinals and 0^ This talk will cover some of the basic Large cardinal definitions and axioms (e.g. http://www.math.wisc.edu/~gpslogic/fall2005.html

home schedule links uw math department math library swlc Fall 2005 Schedule - Thursday, 8 September 2005: Asher Kach on "An Incomplete History of Logic" - Thursday, 15 September 2005: Sasha Rubin on "An Introduction to Automatic Structures" - Thursday, 22 September 2005: Alex Raichev on "Relative Randomness" - Thursday, 29 September 2005: Rob Owen on "Large Cardinals and 0^#" - Thursday, 6 October 2005: Kathleen Kiernan on "The August 2005 Logic Qualifying Exam" - Thursday, 13 October 2005: David Milovich on "Connectifications" - Thursday, 20 October 2005: Dan McGinn on "First Order Definability in Modal Logic" - Thursday, 27 October 2005: Will not meet - SWLC (David Fremlin) - Thursday, 3 November 2005: Will not meet - Thursday, 10 November 2005: David Milovich on "A Homogeneous Path-Connected Compactum of Cellularity c" - Thursday, 17 November 2005: Chris Alfeld on "Relativizations of P vs NP" - Thursday, 24 November 2005: Will not meet - Thanksgiving - Thursday, 1 December 2005: Will not meet - Thursday, 8 December 2005: Ben Ellison on "Jet Spaces and Model Theory"

41. Recent Advances In Core Model Theory (Variant) Assume there are arbitrarily Large Woodin cardinals. In terms of Large cardinal axioms, characterize those LE successor cardinals with the http://www.math.cmu.edu/~eschimme/AIM/Problems-temp.html

Recent Advances in Core Model Theory Open problems (under construction) Determine the consistency strength of "every real has a sharp + u " where u is the second uniform indiscernible. Steel and Welch showed that a strong cardinal is a lower bound. It is not known how to use the hypothesis u to build models with more large cardinals than this even if granted that K exists. in L( R ) is constructible from a real". References: Steel, J. R., and Welch., P. D., absoluteness and the second uniform indiscernible , Israel J. Math. 104 (1998) 157-190 Woodin, W. H., The axiom of determinacy, forcing axioms and the nonstationary ideal , DeGruyter series in logic and its applications, vol. 1, 1999 set of reals called C . It also follows from PD that for each n n . Is it true that C equivalent to a mastercode of M C is the set of reals in M = L . C equivalent to a mastercode of M = L . C is the set of reals in M The general question is how this pattern continues at the odd levels. References: Kechris, A.

42. The Higher Infinite: Large Cardinals In Set Theory From Their Beginnings - Libro The Higher Infinite Large cardinals in Set Theory from Their Beginnings, Akihiro Kanamori, A. Kanamori. The theory of Large cardinals is currently a broad http://www.libreriauniversitaria.it/higher-infinite-large-cardinals-set/book/978

PowerSearch: Libri Italiani Libri Inglesi Libri Tedeschi DVD Videogames Tutti i reparti The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings di Akihiro Kanamori A. Kanamori Prezzo: Questo libro ha diritto alla spedizione gratuita Leggi i dettagli Disponibilità: Normalmente disponibile in 6/8 giorni lavorativi Metti nel carrello (Puoi sempre toglierlo dopo) Descrizione The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths  leading  to the frontiers of contemporary research. A "genetic" approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterprise but also become prepared to pursue research in several specific areas by studying the relevant sections. Dettagli del libro Titolo: The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings Autori: Akihiro Kanamori A. Kanamori

43. Large Cardinal Property - Wikipedia, The Free Encyclopedia In the mathematical field of set theory, a Large cardinal property is a certain kind of property of transfinite cardinal numbers. http://en.wikipedia.org/wiki/Large_cardinal

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Large cardinal property From Wikipedia, the free encyclopedia (Redirected from Large cardinal Jump to: navigation search For a list of examples, see list of large cardinal properties In the mathematical field of set theory , a large cardinal property is a certain kind of property of transfinite cardinal numbers . Cardinals with such properties are, as the name suggests, generally very "large" (for example, bigger than aleph zero , bigger than the cardinality of the continuum , et cetera). The proposition that such cardinals exist cannot be proved in the most common axiomatization of set theory, namely ZFC , and such propositions can be viewed as ways of measuring how "much", beyond ZFC, one needs to assume to be able to prove certain desired results. In other words, they can be seen, in Dana Scott 's phrase, as quantifying the fact "that if you want more you have to assume more". There is a rough convention that results provable from ZFC alone may be stated without hypotheses, but that if the proof requires other assumptions (such as the existence of large cardinals), these should be stated. Whether this is simply a linguistic convention, or something more, is a controversial point among distinct philosophical schools (see Motivations and epistemic status below).

44. [FOM] What Makes A Large Cardinal Axiom Plausible? On Thursday 06 May 2004 328 pm, Timothy Y. Chow wrote I want to pick up on Roger Bishop Jones s suggestion that what makes a Large cardinal axiom http://cs.nyu.edu/pipermail/fom/2004-May/008125.html

[FOM] What makes a large cardinal axiom plausible? Roger Bishop Jones rbj01 at rbjones.com Fri May 7 02:38:04 EDT 2004 Previous message: [FOM] What makes a large cardinal axiom plausible? Next message: [FOM] consistency of PA? Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] I want to pick up on Roger Bishop Jones's suggestion that what makes a large cardinal axiom plausible is that it "merely" sets a lower bound on the size of the cumulative hierarchy. From the observation that some effects of large cardinal Previous message: [FOM] What makes a large cardinal axiom plausible? Next message: [FOM] consistency of PA? Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

45. Large Capitalization Stocks - What Does LCS Stand For? Acronyms And Abbreviation Large Capitalization Stocks Large car Large cardinal Large cardinal axiom Large cardinal hypotheses Large cardinal hypothesis http://acronyms.thefreedictionary.com/Large Capitalization Stocks

Domain='thefreedictionary.com' word='LCS' Printer Friendly 728,491,308 visitors served. TheFreeDictionary Google Word / Article Starts with Ends with Text subscription: Dictionary/ thesaurus Medical dictionary Legal dictionary Financial dictionary Acronyms Idioms Encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia LCS (redirected from Large Capitalization Stocks 0.04 sec. Acronym Definition LCS Label Controlled Switch (Cisco) LCS Laboratory Computer System (EPA) LCS Laboratory Control Sample LCS Laboratory for Computer Science (MIT) LCS LAHET Code System LCS Lake Chelan Shores LCS Land Combat Systems LCS Landing Craft, Support LCS Lane Control Signs (intelligent transportation systems) LCS LANTIRN Control Software LCS Large Capacity Storage LCS Large Capitalization Stocks LCS Las Canas, Costa Rica (Airport code) LCS Laser Communication System LCS laser communication systems LCS Laser Countermeasure System LCS Laser Cross Section LCS Laser Crosslink System LCS Last Clan Standing (gaming) LCS Last Comic Standing (TV series) LCS Launch Control Station LCS LCAC Control Ship LCS League Championship Series (Baseball) LCS Leakage Collection System LCS Learning Classifier System LCS Left Control Strategy LCS Lewis Carroll Society (UK) LCS Liberty City Stories (Grand Theft Auto game) LCS Library Circulation System LCS Libyan Cardiac Society LCS Life Cycle Selling LCS Life Cycle Status LCS Life Cycle Support LCS Lifescape Community Services LCS Lifetime Cancer Screening LCS Lightwave Communication Systems LCS Lightweight Camouflage System LCS Limited Concentrated Sweets (diet) LCS Limiting Control Settings

46. Earth Charms - Large Cardinal Charm Large Cardinal Charm. Dimensions Width 9/16in, Height 9/16in. Price $9.00. Qty. Large cardinal charm made of sterling silver. http://www.earthcharms.com/LGcardinal.htm

Bird Charms Flora Charms Aquatic Animals Mammals ... Other Cardinals Cardinalis This bird is named for the red robed and red capped Catholic priests of medieval Europe. They live in moderate climates of Europe and North America, tending to nest in one place. The male feeds the female insects and plant seeds when she is nesting and protecting the chicks. Their whistle is very distinctive. Home View Cart About Us Contact Us ... Links Related Products: Lg. Cardinal Charms on Earrings Sm. Kingfisher Charm Related Galleries: Bird Charms Large Charms Large Cardinal Charm Dimensions Width 9/16in, Height 9/16in Price: Qty Large cardinal charm made of sterling silver. Return to Gallery Small Charms Small Charms on Earrings Small Charms on Earring with Gems ... Large Charms on Necklaces To see more jewelery by Helen Chantler visit Reflective Images, Inc.