Geometry.net Online Store

1. 03E: Set Theory 03E02 Partition relations; 03E04 Ordered sets and their cofinalities; pcf theory; 03E05 Other combinatorial set theory; 03E10 Ordinal and cardinal http://www.math.niu.edu/~rusin/known-math/index/03EXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 03E: Set theory Introduction Naive set theory considers elementary properties of the union and intersection operators Venn diagrams, the DeMorgan laws, elementary counting techniques such as the inclusion-exclusion principle, partially ordered sets, and so on. This is perhaps as much of set theory as the typical mathematician uses. Indeed, one may "construct" the natural numbers, real numbers, and so on in this framework. However, situations such as Russell's paradox show that some care must be taken to define what, precisely, is a set. However, results in mathematical logic imply it is impossible to determine whether or not these axioms are consistent using only proofs expressed in this language. Assuming they are indeed consistent, there are also statements whose truth or falsity cannot be determined from them. These statements (or their negations!) can be taken as axioms for set theory as well. For example, Cohen's technique of forcing showed that the Axiom of Choice is independent of the other axioms of ZF. (That axiom states that for every collection of nonempty sets, there is a set containing one element from each set in the collection.) This axiom is equivalent to a number of other statements (e.g. Zorn's Lemma) whose assumption allows the proof of surprising even paradoxical results such as the Banach-Tarski sphere decomposition. Thus, some authors are careful to distinguish results which depend on this or other non-ZF axioms; most assume it (that is, they work in ZFC Set Theory).

2. MSC 2000 : CC = Ordered 03E04 Ordered sets and their cofinalities; pcf theory Nouveau code MSC 2000. Codes MSC1991 affiliés 03E05, 03E10, 04A10, 04A20 http://portail.mathdoc.fr/cgi-bin/msc2000.py?L=fr&T=Q&C=msc2000&CC=Ordered

3. List For KWIC List Of CCS 1998 And MSC2000 Phrases Ordered sets representations of quivers and partially 16G20 Ordered sets and their cofinalities; pcf theory 03E04 Ordered spaces linearly Ordered http://www.math.unipd.it/~biblio/kwic/msc-acm/cm-kl_11_40.htm

operator equations (general) # methods for solving nonlinear operator ideals operator ideals (nuclear, $p$-summing, in the Schatten - von_Neumann classes, etc.) # operators belonging to operator inequalities operator interfaces I.2.9.e operator means, shorted operators, etc. operator methods in interpolation, moment and extension problems operator sine and cosine functions and higher-order Cauchy problems operator spaces (=matricially normed spaces) operator spaces and completely bounded map operator theory 47-XX operator theory # constructive operator theory # fuzzy operator theory # miscellaneous applications of operator theory # nonstandard operator theory # operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory # other (nonclassical) types of operator theory (spectral, Fredholm, etc.) # several-variable operator theory in probabilistic metric linear spaces operator theory in quantum theory, including spectral analysis # selfadjoint operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory

4. WebChanges < Mizar < Mizar TWiki 03E Set theory Section P S 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 http://wiki.mizar.org/cgi-bin/twiki/view/Mizar/WebChanges

Skip to topic Skip to bottom Jump: Mizar Mizar Web Mizar Web Home Changes Index Search Webs Main Mizar Sandbox TWiki ... Test My links My home page edit Edit Attach ... Printable Mizar.WebChanges r1.1 - 08 Aug 2001 - 05:20 - PeterThoeny topic end Skip to actions Results from Mizar web WebStatistics TWikiGuest 20 Dec 2007 - 20:51 Statistics for TWiki.Mizar Web Month: Topic views: Topic saves: File uploads: Most popular topic views: Top contributors for topic save and uploads: Dec 2007 3678 ... MizarSyntax GrzegorzBancerek 13 Dec 2007 - 11:15 Mizar syntax Main.GrzegorzBancerek 12 Dec 2007 Redefinition-Block cannot repeat (it is intention, not practice(?)). In Identify-Registration, the intention is to ... ManualPl GrzegorzBancerek 13 Dec 2007 - 11:03 Podr #281;cznik Wersja angielska Mizar co to jest? Mizar jest proof checkerem wyposa #380;onym we w #322;asny j #281;zyk i bibliotek #281; artyku #322; #243;w matematycznych ... ReviewerCriteria AdamGrabowski 13 Dec 2007 - 10:59 Tu powinny sie znalezc kryteria, ktorymi maja sie kierowac recenzenci przy recenzji artykulu do FM (i MML) Main.GrzegorzBancerek 09 Dec 2005 0. W bibie obowiazkowe ... ManualPlCorrelates GrzegorzBancerek 13 Dec 2007 - 10:56 Podr #281;cznik Korelaty semantyczne Korelaty semantyczne s #261; postaciami normalnymi systemu redukcji z nast #281;puj #261;cymi regu #322;ami: wzorzec redukt not ...

5. 03Exx 03E04, Ordered sets and their cofinalities; pcf theory. 03E05, Other combinatorial set theory. 03E10, Ordinal and cardinal numbers. 03E15, Descriptive set http://www.impan.gov.pl/MSC2000/03Exx.html

Set theory Partition relations Ordered sets and their cofinalities; pcf theory Other combinatorial set theory Ordinal and cardinal numbers Descriptive set theory [See also Cardinal characteristics of the continuum Other classical set theory (including functions, relations, and set algebra) Axiom of choice and related propositions Axiomatics of classical set theory and its fragments Consistency and independence results Other aspects of forcing and Boolean-valued models Inner models, including constructibility, ordinal definability, and core models Other notions of set-theoretic definability Continuum hypothesis and Martin's axiom Large cardinals Determinacy principles Other hypotheses and axioms Nonclassical and second-order set theories Fuzzy set theory Applications of set theory None of the above, but in this section

6. Mhb03.htm 03Exx, Set theory. 03E02, Partition relations. 03E04, Ordered sets and their cofinalities; pcf theory. 03E05, Other combinatorial set theory http://www.mi.imati.cnr.it/~alberto/mhb03.htm

03-XX Mathematical logic and foundations General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. General logic Classical propositional logic Classical first-order logic Higher-order logic and type theory Subsystems of classical logic (including intuitionistic logic) Abstract deductive systems Decidability of theories and sets of sentences [See also Foundations of classical theories (including reverse mathematics) [See also Mechanization of proofs and logical operations [See also Combinatory logic and lambda-calculus [See also Logic of knowledge and belief Temporal logic ; for temporal logic, see ; for provability logic, see also Probability and inductive logic [See also Many-valued logic Fuzzy logic; logic of vagueness [See also Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

7. HeiDOK 03Exx Set theory ( 0 Dok. ) 03E02 Partition relations ( 0 Dok. ) 03E04 Ordered sets and their cofinalities; pcf theory ( 0 Dok. http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03E&anzahl

8. MSC 2000 : CC = Set 03D65 Highertype and set recursion theory; 03Exx Set theory; 03E04 Ordered sets and their cofinalities; pcf theory Nouveau code MSC 2000 http://www-mathdoc.ujf-grenoble.fr/cgi-bin/msc2000.py?CC=set&L=fr

9. PlanetMath: Cofinality The cofinality of any totally Ordered set is necessarily a regular cardinal. Set theory Ordered sets and their cofinalities; pcf theory) http://planetmath.org/encyclopedia/RegularCardinal.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About cofinality (Definition) Definitions Let be a poset . A subset is said to be cofinal in if for every there is a such that . A function is said to be cofinal if is cofinal in . The least cardinality of a cofinal set of is called the cofinality of . Equivalently, the cofinality of is the least ordinal such that there is a cofinal function . The cofinality of is written , or Cofinality of totally ordered sets If is a totally ordered set , then it must contain a well-ordered cofinal subset which is order-isomorphic to . Or, put another way, there is a cofinal function with the property that whenever For any ordinal we must have , because the identity map on is cofinal. In particular, this is true for cardinals , so any cardinal either satisfies , in which case it is said to be regular , or it satisfies , in which case it is said to be singular The cofinality of any totally ordered set is necessarily a regular cardinal.

10. MSC 2000 : CC = Order 03C68 Other classical firstorder model theory; 03C85 Second- and higher-order model theory; 03E04 Ordered sets and their cofinalities; pcf theory New MSC http://mathdoc.emath.fr/cgi-bin/msc2000.py?L=en&T=Q&C=msc2000&CC=Order

11. Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical Logic A edit 03C64 Model theory of Ordered structures; ominimality. Needs to be merged 1. . edit 03E04 Ordered sets and their cofinalities; pcf theory http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Mathematics/PlanetMath_Exchan

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations From Wikipedia, the free encyclopedia Wikipedia:WikiProject Mathematics PlanetMath Exchange Jump to: navigation search This page provides a list of all articles available at PlanetMath in the following topic: 03-XX Mathematical logic and foundations This list will be periodically updated. Each entry in the list has three fields: PM WP Status status entries are: Status means PM article N not needed A adequately covered C copied M merged NC needs copying NM needs merging Please update the WP and Status fields as appropriate. if the WP field is correct please remove the qualifier "guess". If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link. If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry. If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable. Don't forget to include the relevant template if you copy over text or feel like an external link is warranted See the main page for examples and usage criteria.

12. New Classes 03E04, Ordered sets and their cofinalities; pcf theory, 03E05, 03E10, 04A10, 04A20. 03E17, Cardinal characteristics of the continuum, 03E05, 03E10, 03E15, http://www.ams.org/mathweb/msc2000/2000to1991.html

Conversion tables between the 1991 and 2000 versions of the Mathematics Subject Classification (MSC) Items appearing in the 2000a (January) and later issues of Mathematical Reviews and in the 2000:01 and later issues of Current Mathematical Publications are classified using , which is a revision of the 1991 MSC . The great majority of the over 5000 classification codes in the 1991 MSC remain valid in MSC2000. However, over 400 classification codes from the 1991 MSC do not appear in MSC2000 and there are over 1000 new codes in MSC2000. To help users of the MSC, the editors of Mathematical Reviews have constructed conversion tables. One table gives for each 1991 code that does not appear in MSC2000 the code(s) in MSC2000 that are most likely to be used for items that would previously have been classified using the code that is now invalid. The other table gives for each new code in MSC2000 the codes in the 1991 MSC that are most likely to have been used earlier for items classified using the new code. The description associated with each code can be found by clicking on 1991 MSC or , as appropriate.

13. Mathematics Subject Classification 1998 03E04 Ordered sets and their cofinalities; pcf theory) = 03E04 Ordered sets and their cofinalities; pcf theory 03E20 Other classical set theory (including http://ftp.fi.muni.cz/pub/muni.cz/EMIS/MSC2000/change.html

07:45 Thu 20 May 1998 33-XX - corrected referral text (also in index.html): ION 34Gxx - add spaces after commas in referral list: ION 35Lxx - fix redundant referral text: ION 35Mxx - fix shortened subsection title: ION 35Nxx - fix bracket in referral text: ION 35Sxx - remove spurious newline in header text: led to wrong font in text: ION 46Exx - fix bracketing and braces in referral line: ION 46Fxx - fix comma in referral line: ION 46Lxx - fix double bracket in referral: ION 53Cxx - fix headline referral: ION 53Dxx - correct ? in referral: ION 54Cxx - remove redundant 54C45 lines: ION 55Mxx - fix referral found in wrong place: ION 57Sxx - fix referral line: ION 58-XX - remove extra > in title: ION 60-XX - change previous pointer to 58: ION index.html - fix HTML syntax [also for ../msc2000.html] and items below: ION 74axx (in 76-XX entry; merged lines too) => 74Axx CREATED change.html file and added pointer text to the bottom of the blurb in index.html: ION 91Cxx - removed hyphen (previously inserted for consistency): ION 91C15 One- and multi-dimensional scaling => 91C15 One- and multidimensional scaling 11Nxx - fixed Turan's accent: ION 21 May 1998 80Axx - added line and corrected a capitalization: RAS, ALG, ION

14. MSC 2000 : CC = Ordered 03E04 Ordered sets and their cofinalities; pcf theory Nouveau code MSC 2000. Codes MSC1991 affiliés 03E05, 03E10, 04A10, 04A20. 06XX Order, lattices, http://math-doc.ujf-grenoble.fr/cgi-bin/msc2000.py?L=fr&T=Q&C=msc2000&CC=Ordered

15. 359/369 (Total 5522) NO 152 03E04 Ordered Sets And Translate this page 152, 03E04, Ordered sets and their cofinalities; pcf theory. 151, 03E02, Partition relations. 150, 03Dxx, Computability and recursion theory http://www.mathnet.or.kr/mathnet/msc_list.php?mode=list&ftype=&fstr=&page=359

16. Browse MSC2000 Ordered sets and their cofinalities; pcf theory, related Other classical set theory including functions, relations, and set algebra, related http://www.zblmath.fiz-karlsruhe.de/MATH/msc/zbl/msc/2000/03-XX/03Exx/dir

Contact Search Browse Instructions ... Main Changes 75th anniversary Zentralblatt MATH Home Facts and Figures Partners and Projects Subscription Service Database Gateway Database Mirrors Reviewer Service Classification ... Serials and Journals database Miscellanea Links to the Mathematical World Display Text version Printer friendly page Internal Browse MSC2000 - by section and classification TOP MSC2000 - Mathematics Subject Classification Scheme 03-XX Mathematical logic and foundations Set theory Classification Topic X-ref Partition relations related... Ordered sets and their cofinalities; pcf theory related... Other combinatorial set theory related... Ordinal and cardinal numbers related... Descriptive set theory [See also related... Cardinal characteristics of the continuum related... Other classical set theory including functions, relations, and set algebra related... Axiom of choice and related propositions related...

17. MSC2000: Parent = (03Exx) 03E04 Ordered sets and their cofinalities; pcf theory New MSC2000 code. Related MSC1991 codes 03E05, 03E10, 04A10, 04A20. 03E05 Other combinatorial set http://jfm.sub.uni-goettingen.de/cgi-bin/jfmscen?form=/JFM/en/quick.html&zb=/cgi

18. Zentralblatt MATH - MSC 2000 - Search And Browse 03Exx Set theory ZMATH. 03E02 Partition relations ZMATH. 03E04 Ordered sets and their cofinalities; pcf theory ZMATH. 03E05 Other combinatorial set http://www.zentralblatt-math.org/msc/search/?pa=03Exx

19. MSC2000: Parent = (03Exx) 03E04 Ordered sets and their cofinalities; pcf theory Nouveau code MSC2000. Codes MSC1991 affiliés 03E05, 03E10, 04A10, 04A20 http://www-zb.univ-mrs.fr/cgi-bin/zmscfr?form=/ZMATH/fr/zmath.html&zb=/cgi-bin/z

20. 03Exx 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 Ordinal and cardinal numbers http://202.38.126.65/mirror/www.ams.org/03Exx-1.html

Top Set theory 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 Ordinal and cardinal numbers 03E15 Descriptive set theory [See also ] 03E17 Cardinal characteristics of the continuum 03E20 Other classical set theory (including functions, relations, and set algebra) 03E25 Axiom of choice and related propositions 03E30 Axiomatics of classical set theory and its fragments 03E35 Consistency and independence results 03E40 Other aspects of forcing and Boolean-valued models 03E45 Inner models, including constructibility, ordinal definability, and core models 03E47 Other notions of set-theoretic definability 03E50 Continuum hypothesis and Martin's axiom 03E55 Large cardinals 03E60 Determinacy principles 03E65 Other hypotheses and axioms 03E70 Nonclassical and second-order set theories 03E72 Fuzzy set theory 03E75 Applications of set theory 03E99 None of the above, but in this section Version of December 15, 1998

21. Computing And Information Technology Interactive Digital Educational Library Rep AMS Mathematics Subject Classification 2000 version Mathematical logic and foundations Set theory Ordered sets and their cofinalities; pcf theory http://www.citidel.org/?op=cbrowse&scheme=MSC2000&category=03-XX:03Exx:03E04

22. MathGuide - OPAC Subject Catalog 03E02 Partition relations; 03E04 Ordered sets and their cofinalities; pcf theory; 03E05 Other combinatorial set theory; 03E10 Ordinal and cardinal numbers http://www.mathguide.de/cgi-bin/ssgfi/navigator2.pl/db=math/type=gok/pattern=all

Browse the GBV OPAC by MSC 2000 This is a browse interface to the union catalogue of the Common Library Network GBV based on the MSC 2000 classification. You can browse down to the individual notation, the links available will direct you to the appropriate place in the GBV OPAC, which uses a notation related to, but different from MSC. Note: Not all books available are contained in the online catalogue. Please use the Goettingen State University Library's Alphabetical Catalogue to search for monographs, dissertations and journals missing in the OPAC. Open all categories Close all categories Foundations 00-XX General Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) General mathematics General and miscellaneous specific topics General mathematics Mathematics for nonmathematicians (engineering, social sciences, etc.) Problem books Recreational mathematics Bibliographies External book reviews Dictionaries and other general reference works Formularies Philosophy of mathematics Methodology of mathematics, didactics

23. Googlelinked Mathematics Subject Headings 03Exx Set theory 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory http://www.plambeck.org/oldhtml/mathematics/mathsubjects/index.htm

googlelinks plambeck.org mathematics googlelinks how it works [This page is a work in progress, started 25 June 2004. I'm still figuring out how to automate the creation of this page in the best way, but the great thing is that Google will keep it up to date for me when I'm done!] Googlelinked Mathematics Subject Headings All links dereference through Google's "I'm feeling Lucky." Here's an explanation of what I'm trying to do here. 00–XX GENERAL 00–01 Instructional exposition ( textbooks , tutorial papers, etc.) 00–02 Research exposition ( monographs survey articles 00Axx General and miscellaneous specific topics General mathematics 00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) Problem books Recreational mathematics [See also 97A20] Bibliographies 00A17 External book reviews Dictionaries and other general reference works Formularies Philosophy of mathematics [See also 03A05] 00A35 Methodology of mathematics, didactics [See also 97Cxx, 97Dxx] 00A69 General applied mathematics 00A71 Theory of mathematical modeling 00A72 General methods of simulation Dimensional analysis 00A79 Physics (use more specific entries from Sections 70-86) 00A99 Miscellaneous topics 00Bxx Conference proceedings and collections of papers 00B05 Collections of abstracts of lectures 00B10 Collections of articles of general interest 00B15 Collections of articles of miscellaneous specific content 00B20 Proceedings of conferences of general interest 00B25 Proceedings of conferences of miscellaneous specific interest

24. Catálogo - MSC 2000 Translate this page 03E04, Ordered sets and their cofinalities; pcf theory. 03E05, Other combinatorial set theory. 03E10, Ordinal and cardinal numbers http://catalis.uns.edu.ar/cgi-bin/catalis_pack_demo_devel/wxis?IsisScript=opac/x

25. Search Results For 'ordinal' Translate this page 03E04 Ordered sets and their cofinalities; pcf theory ( 0 Dok. ) * 03E05 Other combinatorial set theory ( 0 Dok. ) * 03E10 Ordinal and cardinal numbers ( 0 http://opus.hbk-bs.de/cgi-bin/htsearch?words=ordinal

26. Biocrawler:WikiProject Mathematics/PlanetMath Exchange/26-XX Real Functions - Bi See 03E04 Ordered sets and their cofinalities; pcf theory. PM partial derivative (http//planetmath.org/?op=getobj from=objects id=841), http://www.biocrawler.com/encyclopedia/Biocrawler:WikiProject_Mathematics/Planet

Inline videos See also: Category: Articles with embedded Videos. Biocrawler:WikiProject Mathematics/PlanetMath Exchange/26-XX Real functions From Biocrawler This page provides a list of all articles available at PlanetMath in the following topic: 26-XX Real functions This list will be periodically updated. Each entry in the list has three fields: PM : The first field is the link to the PlanetMath article, along with the article's object ID. WP : The second field is either a "guessed" link to a correspondingly named Biocrawler article, produced by the script which generated the list, or one or more manully entered links to the corresponding Biocrawler articles on the subject. Status : The third field is the status field, which explains the current status of the entry. The recommended status entires are: Needs to be copied Copied Needs to be merged Merged WP article adequate WP article more complete Not needed on WP Please update the WP and Status fields as appropriate. if the WP field is correct please remove the qualifier "guess". If the corresponding Biocrawler article exists, but the link to it is wrong, please fix the link.

27. SUB Göttingen - Systematische Recherche Im Katalog Der SUB EADC 640, Model theory of Ordered structures; ominimality EADE 040, Ordered sets and their cofinalities; pcf theory http://www.sub.uni-goettingen.de/scripts/gok/browse.php?gok=E&lang=de

28. Fremlin --- Measure Theory 5A2 pcf theory Reduced products of partially Ordered sets; cofinalities of reduced products; covSh(a,b,c,d); Q(a,g). 5A3 Forcing http://www.essex.ac.uk/maths/staff/fremlin/cont5a.htm

of Measure Theory , by D.H.Fremlin Appendix to Volume 5 5A1 Set theory Cardinal arithmetic; D -systems and free sets; partition calculus; transversals; GCH, V=L and the Covering Lemma, squares, Chang's transfer principle; trees. 5A2 Pcf theory Reduced products of partially ordered sets; cofinalities of reduced products; cov Sh a b c d Q a g 5A3 Forcing Forcing notions; forcing languages; the forcing relation; the forcing theorem; Boolean truth values; regular open algebras; discriminating names; L and names for real numbers; forcing with Boolean algebras; iterated forcing; Martin's axiom. 5A4 General topology Cardinal functions; Vietoris topologies; Blumberg's theorem. 5A5 Real analysis Real-entire functions. 5A6 `Later editions only' TeX file. PostScript file (results-only version). Return to contents page. Revised 10.12.07

29. JSTOR Singular Cardinals And The Pcf Theory So unless R R +i, the set pcf A has only one element outside A, and so a meaningful theory of possible cofinalities requires the negation of the singular http://links.jstor.org/sici?sici=1079-8986(199512)1:4<408:SCATPT>2.0.CO;2-5

30. Proceedings Of The Ninth Prague Topological Symposium (2001) Elekés M., Linearly Ordered sets of continuous and Baire 1 functions Gorelic I., Partial orders with singular cofinalities http://www.emis.de/proceedings/TopoSym2001/00.htm

Topology Atlas Document # ppae-00 Proceedings of the Ninth Prague Topological Symposium Contributed papers from the symposium held in Prague, August 19-25, 2001 Edited by Petr Simon This collection of thirty two reviewed articles covers several fields of General Topology. Several contributions represent invited presentations at the Ninth Prague Topological Symposium. Contents Publication data Acknowledgements Ninth Prague Topological Symposium Participants ... Existence of a sublinear continuous order-preserving function for a noncomplete preorder on a topological vector space pp. 1-8 Some equivalences for Martin's Axiom in asymmetric topology Bruce S. Burdick pp. 9-13 The maximal G-compactifications of G-spaces with special actions V. A. Chatyrko and K. L. Kozlov pp. 15-21 Concerning the dual group of a dense subgroup W. W. Comfort, S. U. Raczkowski and F. Javier Trigos-Arrieta pp. 23-35 van Douwen's problems related to the Bohr topology Dikran Dikranjan pp. 37-50 On Tychonoff-type hypertopologies Georgi Dimov, Franco Obersnel and Gino Tironi pp. 51-70

31. TOPOSYM, Prague Topological Symposium Elekés M. Linearly Ordered sets of continuous and Baire 1 functions Gorelic I. Partial orders with singular cofinalities http://toposym.mff.cuni.cz/history/2001.html

TOPOSYM 2001 9th Prague topological symposium, Czech Republic August 19 - 25, 2001 main page location program proceedings and abstracts ... Toposym 1961 The organisers: S. Donaldson (representative of IMU) M. Husek (chairman) B. Balcar (vicechairman) P. Simon (secretary) J. Coufal P. Holicky O. Kalenda A. Klic J. Pelant R. Rohackova (treasurer) V. Trnkova International Conference on General Topology and its Relations to Modern Analysis and Algebra was organized under the auspices of: Mathematical Institute of Czechoslovak Academy of Sciences, International Mathematical Union, in cooperation with: Department of Mathematics of Prague Institute of Chemical Technology, Department of Mathematics of University of Economics, Faculty of Mathematics and Physics of Charles University . Toposym was partly sponsored by International Mathematical Union, by grants of organizers, by Czech Airlines, by Elsevier and by Conforg (A. Kotesovcova). The Symposium was attended by 209 mathematicians from 35 countries. The scientific program consisted of 41 lectures invited by the organizing committee, 103 oral contributions presented in four parallel sections, 14 posters and 9 enlarged abstracts. Many contributions together with abstracts are published at Topology Atlas . The conference took place at an areal of University of Economics (scientific program) and of Prague Institute of Chemical Technology (accommodation and meals) at the southern part of Prague. During the conference, several social and cultural events were organized (welcome and farewell rauts, a sightseeing tour in Prague, an organ concert in a church, guided tours in Prague for accompanying persons, and a wholeday tour to a crystal-glass factory at Nizbor, a classicist castle Kozel near Pilsen with a inner in a country farm restaurant. You can also see some

32. Abstracts For Seminar Talks At The KGRC Matteo Viale, Reflection principles and pcf theory Abstract . the possible scenarios to change cofinalities while preserving forcing axioms or strongly http://www.logic.univie.ac.at/abstracts.html

Abstracts for seminar talks at the KGRC Philip Welch, In and around the Ramsey property: Abstract Recent work on the Mutual Stationarity property has prompted looking at some finite sequence "mutual stationarity" of subsets of omega_1 and omega_2. We discuss some joint work with I. Sharpe on this, related also to mild strengthenings of the Chang Property; some further topics in the Jonsson/Ramsey hierarchy may be mentioned if time permits. Vladimir Kanovei, Lebesgue measure and the coin-tossing game: Abstract And G bets on every next move of C. Beginning with the initial balance say $1, G can bet any amount less than the current balance on one of two possible moves of C (0 or 1), and if C makes that move then the balance accordingly increases by the amount of bet. Otherwise the balance decreases. The final outcome of the game can be defined in terms of the limit of the supremum of the balance values. And it turns out that the existence of certain strategies for G and C characterizes the Lebesgue measure characteristics of the set A. In brief, the smaller A is the bigger gains Casino can guarantee. Matteo Viale, Reflection principles and pcf theory: Abstract

33. 9th Prague Topological Symposium 1996 Linearly Ordered sets of continuous and Baire 1 functions Recent progress in the theory of topological semigroups and the algebra of $\beta S$. Höhle U. http://www.karlin.mff.cuni.cz/~mhusek/cd/history/09-2001.html

9th Prague Topological Symposium (August 19 - 25, 2001) International Conference on General Topology and its Relations to Modern Analysis and Algebra was organized under the auspices of: Mathematical Institute of Czechoslovak Academy of Sciences International Mathematical Union in cooperation with: Department of Mathematics of Prague Institute of Chemical Technology Department of Mathematics of University of Economics, Faculty of Mathematics and Physics of Charles University The organizers S. Donaldson, (representative of IMU) M. Hušek, (chairman) B. Balcar, (vicechairman) P. Simon, (secretary) J. Coufal, P. Holický, O. Kalenda A. Klíè, J. Pelant, R. Roháèková (treasurer) V. Trnková, Toposym was partly sponsored by International Mathematical Union, by grants of organizers, by Czech Airlines, by Elsevier and by Conforg (A. Kotìšovcová). The Symposium was attended by 209 mathematicians from 35 countries. The scientific program consisted of 41 lectures invited by the organizing committee, 103 oral contributions presented in four parallel sections, 14 posters and 9 enlarged abstracts. Many contributions together with abstracts are published at Topology Atlas The conference took place at an areal of University of Economics (scientific program) and of Prague Institute of Chemical Technology (accommodation and meals) at the southern part of Prague.

34. Scientific Commons Saharon Shelah This paper deals with variety of problems in pcf theory and infinitary .. between sets of finitary relations on a base set A and their automorphisms. http://en.scientificcommons.org/saharon_shelah

<`ƒ®?xqoÿÑ[hݸñíÚ΍÷î³ï=ÙgÐ;Lé§7n <wîï, <6h,¬§¶¦j×kµëÕ½hÝm -dŸ-RðѹîhúÙ E±cPh‚¾ U?ãÇÔèžÀ°Ì-Nþ²'ýœšÉ8 w©uÂI€ÜKxq„t¼]òN <2T8ά’`—lQ;0ðú×ôĨ <‹ap€°BÀcµ•¸™*¶+µ¿ <÷l5eW_ŒQ°áw9Z¥sç莟/µ†!–;+(†J Á©ÊbwÞFè€p¢°ÏÐÖ <×æ kà ó3H4#P›à ½óo¢v²G) $Ò©™¬ý´ FJù±È#ˆblŽ.ɓ¦b5N›ë] æi󎵠­#øÓÂðPm%Ö2‚ß9¨ˆk™>áwÆ£ÍLvSþž©dg)ô‰Hš <ƶšæÜÌÓj <êܳ” anOØ５q/yæ‚w­ÜxŒƒ£‡]ù1Ú4›ÑÄ ÷•/s#w‘ƒb <’õš®5ƒÖœ_ZΉN¦Û›u÷‘„U < ”g‘ØLrʲØÛ+¿_hB9nXÛ³jùÚOß%íãå=ooåѪ¿ÇSŽPqÒÂ~í=ŽK’qÚ¥­8 »iÙ¤zÂì <ÿ’]òúžüE(Mt'»â ª6=Á°á¾9ÇB <ÂQô~¿OL¿ÝÕ*֊ev³×žxᮘÌ­½Úü¸èîdÒ âÙÖñ›µÆö1Éf²~õà ³vë?e „ý.œY~·òèÙò;_†¾C0 <‚íc]*Ù¾hŠí÷î=¨r!^faÙ;! <Cjüƒ½¯¾•Œ„‰z%Ð`eiØ b" ®,ÎZ‘Fº-; U°´½/ 9Š©¿©¶)Nt  ó`—ßiG;öë¢æ ù†$µ8mhQ–fö!ìÁjÕ! -,à¥A-!ߗãxš»§œÄmÁ‰È^(¬·ü5'”W°Oƒ§ d‰Š$¾pÄþ,!; L <Ÿç ~²ü²;­›eŽ™e=œ×À²aC6Eï_PÁ³¤ÞÁÌ  CãaÔûõñ‡ð <ÚÏQœ$ <7Xvµ§ÆŠ‚XÌ)Y¨wLˆ,Àò¶œ/Tª£ž¢H Fu’ð¨0Î$Ò÷)½Î”KB· <‹ÂuƒyNÚ@®‰ø_lŽ¼æÜÖòi³ôÕªÍÕªÇC5µÜÂûƒ·f^ùÖùù®uˆ›xC <-¯ PÔD`vuU4ØØ=°+ £Ïéъ¬G¹d <êἐHŠØ—ž—9Áɔx–F ¹Úq‡²F,@‘ <–iÜ£~ŸÛ̗A!¬)©Õ§ 6ÂÄ –ä佚a¦Ý(•ÌjÐÀÁ‹CΎñZþè$‡^8@qç:ýÜ;ºü`¶Sú­÷΂­÷S[”Ôœ¡÷äÉú@ÓÉ7û7¿Ùۉn¤‚þ÷øƒ#žþý¿£Ae$.êъ€j;ã‚âWOý.~áRØBuW'l¢`=ro‡*€¯ÜXÛ

35. Category:Set Theory [Definition] The abbreviation pcf stands for possible cofinalities . click for more; Partially Ordered setIn mathematics, a partially Ordered set (or poset for http://www.wikimirror.com/Category:Set_theory

Category:Set theory information on Wikimirror.com Read below for information on Category:Set theory Search Set theory Set theory is the mathematical theory of sets, which represent collections of abstract objects. It has a central role in modern mathematical theory, providing the basic language in which most of mathematics is expressed. For more information on set theory in Wikipedia, see: Set gives a basic introduction to elementary set theory. Naïve set theory is the original set theory developed by mathematicians at the end of the 19th century. Zermelo set theory is the theory developed by the German mathematician Ernst... [click for more] is any of a number of subtly different things in mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers". Mathematical knowledge is constantly growing, through research and application, but mathematics itself is not usually considered a natural science. One reason is that mathematical knowledge is revised and updated in a different way; though arguably founded on experiment in some manner, it is not comparable to the natural sciences in this respect. ... [click for more] Naive set theory Naive set theory1 is distinguished from axiomatic set theory by the fact that the former regards sets as collections of objects, called the elements or members of the set, whereas the latter regards sets only as that which satisfies certain axioms. Sets are of great importance in mathematics; in fact, in modern formal treatments, every mathematical object (numbers, relations, functions, etc.) is defined in terms of sets....

36. Set Theory In mathematics, especially order theory, a partially Ordered set (or poset stands for possible cofinalities . more on Wikipedia about pcf theory http://www.shortopedia.com/S/E/Set_theory__page5

Set theory In mathematics a pairing function is a process to uniquely encode two natural numbers into a single natural number. ...more on Wikipedia about "Pairing function" This article pertains to functions in mathematics and computer science. For other usages see function (disambiguation). ...more on Wikipedia about "Partial function" In mathematics, especially order theory, a partially ordered set (or poset for short) is a set equipped with a partial order relation. This relation formalizes the intuitive concept of an ordering, sequencing, or arrangement of that set's elements. Such an ordering does not necessarily need to be total, that is, it need not guarantee the mutual comparability of all objects in the set. ...more on Wikipedia about "Partially ordered set" In mathematics, a partition of a set X is a division of X into non-overlapping " parts " or " blocks " or " cells " that cover all of X . More formally, these "cells" are both collectively exhaustive and mutually exclusive with respect to the set being partitioned. ...more on Wikipedia about "Partition of a set"

37. Annals Of Pure And Applied Logic Uniqueness of the implication for totally Ordered MValgebras .. Exact Upper Bounds and Their Uses in Set theory. by Menachem Kojman v. 92 i. 3 p. http://wotan.liu.edu/docis/dbl/apuapl/index.html

The Digital Librarian's Digital Library search D O CIS  Do cuments in  C omputing and I nformation  S cience Home Journals and Conference Proceedings Annals of Pure and Applied Logic On gaps under GCH type assumptions by:  Moti Gitik v. 119 i. 1-3 p. 1 - 18 Thue trees by:  Jerzy Marcinkowski, Leszek Pacholski v. 119 i. 1-3 p. 19 - 59 Apartness spaces as a framework for constructive topology by:  Douglas S. Bridges, Luminita Dediu v. 119 i. 1-3 p. 61 - 83 Delta20 - categoricity in Boolean algebras and linear orderings by:  Charles F. D. McCoy v. 119 i. 1-3 p. 85 - 120

38. Re: Cardinality: A Definition Dealing with singular cardinals leads to the very interesting pcf ( Possible CoFinality or Possible cofinalities ) theory of Shaharon Shelah. http://sci.tech-archive.net/Archive/sci.math/2006-10/msg00754.html

Re: Cardinality: a definition From Date : Mon, 02 Oct 2006 23:55:56 +0300 Jesse F. Hughes wrote: Now there's an interesting question. I doubt you'll be satisfied with knowing just that it's not of cofinality omega, and is greater than Well, I guess you *have* told me something I didn't know (or have forgotten). I didn't recall that cofinality omega had anything to do with the answer. 1) f is defined at alpha only if aleph_alpha is regular it is consistent with ZFC that 2^aleph_alpha = f(alpha) for all alpha for which f(alpha) is defined. This is a famous result of Easton, essentially the first application of forcing with a class sized forcing notion. Dealing with singular cardinals leads to the very interesting PCF ("Possible CoFinality" or "Possible CoFinalities") theory of Shaharon Shelah. "Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus References Re: Cardinality: a definition From: David R Tribble Re: Cardinality: a definition From: Jesse F. Hughes

39. 2003-12-04 Estimating Internal Memory Fragmentation For Java General Set theory. 133145 1942 7 J. Symb. Log. 2003-11-20 Partially Ordered sets Representable by Recursively Enumerable Classes. http://lsdis.cs.uga.edu/projects/semdis/swetodblp/may2007/swetodblp_may_2007_par

Estimating internal memory fragmentation for Java programs. Journal of Systems and Software http://dx.doi.org/10.1016/S0164-1212(02)00048-1 http://www.informatik.uni-trier.de/~ley/db/journals/jss/jss64.html#SkotiniotisC02 Journal of Systems and Software http://dx.doi.org/10.1016/0164-1212(83)90002-X http://www.informatik.uni-trier.de/~ley/db/journals/jss/jss3.html#SalisburyM83 A language and system for making definitions of technical concepts. Journal of Systems and Software http://dx.doi.org/10.1016/0164-1212(91)90087-M http://www.informatik.uni-trier.de/~ley/db/journals/jss/jss14.html#Skuce91 EIS data: findings from an evolutionary study. Journal of Systems and Software http://dx.doi.org/10.1016/S0164-1212(02)00030-4 http://www.informatik.uni-trier.de/~ley/db/journals/jss/jss64.html#Salmeron02 Contingent information systems development. Journal of Systems and Software http://dx.doi.org/10.1016/0164-1212(95)00186-7 http://www.informatik.uni-trier.de/~ley/db/journals/jss/jss33.html#SlootenS96 A study of software metrics. Journal of Systems and Software http://dx.doi.org/10.1016/0164-1212(91)90017-Z

40. CCS1998 ACM Computing Classification System [1998 Version] Http Set theory concepts are used in software engineering and in databases. .. address an important set of welldefined problems, recognizing their strengths http://physjob.nudl.org/~akrowne/citidel/export/citidelclass_20031031.xml

ACM Computing Classification System [1998 version] http://www.acm.org/class/1998/ General Literature A General A.0 Biographies autobiographies Conference proceedings General literary works fiction plays Introductory And Survey A.1 Reference (e.g., dictionaries, encyclopedias, glossaries) A.2 Miscellaneous A.m Hardware B General B.0 Control Structures And Microprogramming B.1 General B.1.0 Control Design Styles B.1.1 Hardwired control Microprogrammed logic arrays Writable control store Control Structure Performance Analysis and Design Aids B.1.2 Automatic synthesis Formal models Simulation Control Structure Reliability, Testing, and Fault-Tolerance B.1.3 Diagnostics Error checking Redundant design Test generation Microprogram Design Aids B.1.4 Firmware engineering Languages compilers Machine independent microcode generation Optimization Verification Microcode Applications B.1.5 Direct data manipulation Firmware support operating systems instruction sets Instruction set interpretation Peripheral control Special purpose Miscellaneous B.1.m

41. 2003-11-20 Simplest Normal Truth Functions. 105-108 1955 20 J 200311-20 Weakly O-Minimal Structures and Some of Their Properties. . The Status of the Axiom of Choice in Set theory with a Universal Set. http://swat.cse.lehigh.edu/resources/data/swetodblp/swetodblp_106.owl

Simplest Normal Truth Functions. J. Symb. Log. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml20.html#Nelson55 Twenty-Fifth Annual Meeting of the Association for Symbolic Logic. J. Symb. Log. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml25.html#Nelson60 Non-Null Implication. J. Symb. Log. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml31.html#Nelson66 Logic of Reduced Power Structures. J. Symb. Log. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml48.html#Nelson83 Lower Bounds for Cutting Planes Proofs with Small Coefficients. J. Symb. Log. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml62.html#BonetPR97 Sur Les Types Des Propositions Composees. J. Symb. Log. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml5.html#Polya40 Meeting of the Association for Symbolic Logic: Sydney, 1984. J. Symb. Log. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml51.html#Staines86 Strongly Majorizable Functionals of Finite Type: A Model for Barrecursion Containing Discontinuous Functionals. J. Symb. Log.

42. ICMS - ICMS - - - MSC Translate this page 152, A ZFC Dowker Space in $\aleph_{\omega +1}$ An Application of pcf theory to Topology(2459-2465 Page), Menachem Kojman ,Saharon Shelah http://mathnet.kaist.ac.kr/mathnet/thesis_author.php?author=Ron A

43. The Bulletin Of Symbolic Logic 10798986 Association For Symbolic Successors of singulars, cofinalities of reduced products of cardinals Large cardinals in set theory from their beginnings, Springer, Berlin, 1994. http://spider.jstor.org:9080/spidergate/metadata?issn=10798986&index=0

44. 01/07/07 Translate this page These sets have the property If S is in P, then P = NP. Many many many NP-complete problems are known (usually expressed in terms of Graph theory, where http://xinjishu.blogspot.com/2007_01_07_archive.html