Table Of Content

This page intentionally left blank SetTheory,Arithmetic,andFoundationsofMathematics: Theorems,Philosophies Thiscollectionofpapersfromvariousareasofmathematicallogicshowcasesthe remarkablebreadthandrichnessofthefield.Leadingauthorsrevealhow contemporarytechnicalresultstouchuponfoundationalquestionsaboutthenatureof mathematics.Highlightsofthevolumeinclude:ahistoryofTennenbaum’stheoremin arithmetic;anumberofpapersonTennenbaumphenomenainweakarithmeticsas wellasonotheraspectsofarithmetics,suchasinterpretability;thetranscriptof Gödel’spreviouslyunpublished1972–1975conversationswithSueToledo,alongwith anappreciationofthesamebyCurtisFranks;HughWoodin’spaperarguingagainst thegenericmultiverseview;AnneTroelstra’shistoryofintuitionismthrough1991; andAkiKanamori’shistoryoftheSuslinprobleminsettheory. Thebookprovidesahistoricalandphilosophicaltreatmentofparticulartheoremsin arithmeticandsettheory,andisidealforresearchersandgraduatestudentsin mathematicallogicandphilosophyofmathematics. JULIETTE KENNEDYisaUniversityLecturerintheDepartmentofMathematics andStatisticsattheUniversityofHelsinki. ROMAN KOSSAKisaProfessorofMathematicsintheGraduateCenterattheCity UniversityofNewYork(CUNY). LECTURE NOTES IN LOGIC APublicationforTheAssociationforSymbolicLogic Thisseriesservesresearchers,teachers,andstudentsinthefieldofsymboliclogic,broadly interpreted.Theaimoftheseriesistobringpublicationstothelogiccommunitywiththeleast possibledelayandtoproviderapiddisseminationofthelatestresearch.Scientificqualityisthe overridingcriterionbywhichsubmissionsareevaluated. EditorialBoard H.DugaldMacpherson,ManagingEditor SchoolofMathematics,UniversityofLeeds JeremyAvigad DepartmentofPhilosophy,CarnegieMellonUniversity VladimirKanovei InstituteforInformationTransmissionProblems,Moscow ManuelLerman DepartmentofMathematics,UniversityofConnecticut HeinrichWansing DepartmentofPhilosophy,Ruhr-UniversitätBochum ThomasWilke InstitutfürInformatik,Christian-Albrechts-UniversitätzuKiel Moreinformation,includingalistofthebooksintheseries,canbefoundat http://www.aslonline.org/books-lnl.html. LECTURE NOTES IN LOGIC 36 Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies Editedby JULIETTE KENNEDY UniversityofHelsinki ROMAN KOSSAK CityUniversityofNewYork associationforsymboliclogic CAMBRIDGE UNIVERSITY PRESS Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,SãoPaulo,Delhi,Tokyo,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9781107008045 AssociationforSymbolicLogic RichardShore,Publisher DepartmentofMathematics,CornellUniversity,Ithaca,NY14853 http://www.aslonline.org (cid:2)c AssociationforSymbolicLogic2011 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2011 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcataloguerecordforthispublicationisavailablefromtheBritishLibrary ISBN978-1-107-00804-5Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. Afraid!OfwhomamIafraid? NotDeath–forwhoisHe? ThePorterofmyFather’sLodge Asmuchabashethme! OfLife?’TwereoddIfear[a]thing Thatcomprehendethme Inoneortwoexistences– AsDeitydecree– OfResurrection?IstheEast AfraidtotrusttheMorn Withherfastidiousforehead? AssoonimpeachmyCrown! —EmilyDickinson Contents Introduction pagexi HistoricalremarksonSuslin’sproblem AkihiroKanamori 1 Thecontinuumhypothesis,thegeneric-multiverseofsets, andthe(cid:2)conjecture W.HughWoodin 13 ω-modelsoffinitesettheory AliEnayatandJamesH.SchmerlandAlbertVisser 43 Tennenbaum’stheoremformodelsofarithmetic RichardKaye 66 Hierarchiesofsubsystemsofweakarithmetic ShahramMohsenipour 80 Diophantinecorrectopeninduction SidneyRaffer 93 Tennenbaum’stheoremandrecursivereducts JamesH.Schmerl 112 Historyofconstructivisminthe20thcentury A.S.Troelstra 150 Averyshorthistoryofultrafinitism RoseM.CherubinandMircoA.Mannucci 180 SueToledo’snotesofherconversationswithGödelin1972–5 SueToledo 200 StanleyTennenbaum’sSocrates CurtisFranks √ 208 Tennenbaum’sproofoftheirrationalityof 2 JoukoVäänänen 226 vii

Description:

This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of T

Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies PDF

243 Pages·2011·1.27 MB·English

by Juliette Kennedy

Checking for file health...

Download

Upgrade Premium

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Download Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies PDF Free - Full Version

by Juliette Kennedy| 2011| 243 pages| 1.27| English

Download Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies by Juliette Kennedy in PDF format completely FREE. No registration required, no payment needed. Get instant access to this valuable resource on PDFdrive.to!

Free Download PDF

About Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies

Detailed Information

Author:	Juliette Kennedy
Publication Year:	2011
Pages:	243
Language:	English
File Size:	1.27
Format:	PDF
Price:	FREE

Download Free PDF

Safe & Secure Download - No registration required

Why Choose PDFdrive for Your Free Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies Download?

100% Free: No hidden fees or subscriptions required for one book every day.
No Registration: Immediate access is available without creating accounts for one book every day.
Safe and Secure: Clean downloads without malware or viruses
Multiple Formats: PDF, MOBI, Mpub,... optimized for all devices
Educational Resource: Supporting knowledge sharing and learning

Frequently Asked Questions

Is it really free to download Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies PDF?

Yes, on https://PDFdrive.to you can download Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies by Juliette Kennedy completely free. We don't require any payment, subscription, or registration to access this PDF file. For 3 books every day.

How can I read Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies on my mobile device?

After downloading Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies PDF, you can open it with any PDF reader app on your phone or tablet. We recommend using Adobe Acrobat Reader, Apple Books, or Google Play Books for the best reading experience.

Is this the full version of Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies?

Yes, this is the complete PDF version of Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies by Juliette Kennedy. You will be able to read the entire content as in the printed version without missing any pages.

Is it legal to download Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies PDF for free?

https://PDFdrive.to provides links to free educational resources available online. We do not store any files on our servers. Please be aware of copyright laws in your country before downloading.

The materials shared are intended for research, educational, and personal use in accordance with fair use principles.