Logic in Tehran PDF
Preview Logic in Tehran
LogicinTehran Sincetheirinception,thePerspectivesinLogicandLectureNotesinLogicserieshave publishedseminalworksbyleadinglogicians.Manyoftheoriginalbooksintheseries havebeenunavailableforyears,buttheyarenowinprintonceagain. Thisvolume,the26thpublicationintheLectureNotesinLogicseries,containsthe proceedingsofthe“WorkshopandConferenceonLogic,Algebra,andArithmetic” heldattheInstituteforStudiesinTheoreticalPhysicsandMathematics(IPM)in Tehran,IraninOctober,2003.Thesepapersaremostlyrevisedandexpandedversions ofthosethatwereoriginallypresentedatthemeeting,andaddressallareasof mathematicallogic.Thebookalsoincludesashorthistoryofmathematicallogicin Iran. Ali EnayatearnedhisPh.D.fromtheUniversityofWisconsin,Madisonin1984. HeiscurrentlyaProfessorofMathematicsatAmericanUniversity,Washington,D.C. Iraj KalantariearnedhisPh.D.fromCornellUniversityin1976andiscurrently ChairoftheDepartmentofMathematicsatWesternIllinoisUniversity. Mojtaba MoniriearnedhisPh.D.fromtheUniversityofMinnesota,Minneapolis in1994.HeiscurrentlyViceHeadoftheSchoolofMathematicsattheInstitutefor StudiesinTheoreticalPhysicsandMathematicsinTehran. LECTURE NOTES IN LOGIC A PublicationofTheAssociation forSymbolicLogic Thisseriesservesresearchers,teachers,andstudentsinthefieldofsymbolic logic,broadlyinterpreted.Theaimoftheseriesistobringpublicationsto thelogiccommunitywiththeleastpossibledelayandtoproviderapid disseminationofthelatestresearch.Scientificqualityistheoverriding criterionbywhichsubmissionsareevaluated. EditorialBoard JeremyAvigad, DepartmentofPhilosophy,CarnegieMellonUniversity ZoeChatzidakis DMA,EcoleNormaleSupérieure,Paris PeterCholak,ManagingEditor DepartmentofMathematics,UniversityofNotreDame,Indiana VolkerHalbach, NewCollege,UniversityofOxford H.DugaldMacpherson SchoolofMathematics,UniversityofLeeds SlawomirSolecki DepartmentofMathematics,UniversityofIllinoisatUrbana–Champaign ThomasWilke, InstitutfürInformatik,Christian-Albrechts-UniversitätzuKiel Moreinformation,includingalistofthebooksintheseries,canbefoundat http://www.aslonline.org/books-lnl.html LECTURE NOTES IN LOGIC 26 Logic in Tehran Proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic, held October 18–22, 2003 Editedby ALI ENAYAT AmericanUniversity,Washington,D.C. IRAJ KALANTARI WesternIllinoisUniversity,Macomb MOJTABA MONIRI TarbiatModaresUniversity,Tehran association for symbolic logic UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 4843/24,2ndFloor,AnsariRoad,Daryaganj,Delhi–110002,India 79AnsonRoad,#06–04/06,Singapore079906 CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781316755747 10.1017/9781316755747 Firstedition©2006AssociationforSymbolicLogicunderlicenseto A.K.Peters,Ltd. Thisedition©2016AssociationforSymbolicLogicunderlicenseto CambridgeUniversityPress. AssociationforSymbolicLogic RichardA.Shore,Publisher DepartmentofMathematics,CornellUniversity,Ithaca,NY14853 http://www.aslonline.org Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy ofURLsforexternalorthird-partyInternetWebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchWebsitesis,orwillremain, accurateorappropriate. TABLEOFCONTENTS Preface............................................................. vii Workshopandconferenceonlogic,algebra,andarithmetic: Tehran,October18–22,2003........................................ ix Foreword........................................................... xi Mohammad-JavadA.Larijani MathematicallogicinIran: Aperspective.......................... xiii SeyedMasihAyatandMojtabaMoniri RealclosedfieldsandIP-sensitivity................................ 1 SeyedMohammadBagheri Categoricityandquantifiereliminationforintuitionistictheories.... 23 DarkoBiljakovic,MikhailKochetov,andSalmaKuhlmann Primesandirreduciblesintruncationintegerpartsofrealclosedfields 42 LouvandenDries Onexplicitdefinabilityinarithmetic............................... 65 AliEnayat Fromboundedarithmetictosecondorderarithmeticvia automorphisms................................................... 87 YuriL.Ershov Local-globalprinciplesandapproximationtheorems............... 114 MehdiGhasemiandMojtabaMoniri Beattysequencesandthearithmeticalhierarchy.................... 126 IrajKalantariandLarryWelch Specker’stheorem,clusterpoints,andcomputablequantum functions......................................................... 134 Franz-ViktorKuhlmann Additivepolynomialsandtheirroleinthemodeltheoryofvalued fields............................................................. 160 v vi tableofcontents Franz-ViktorKuhlmann Densesubfieldsofhenselianfields,andintegerparts................ 204 ShahramMohsenipour ArecursivenonstandardmodelforopeninductionwithGCD propertyandcofinalprimes....................................... 227 MortezaMoniri Modeltheoryofboundedarithmeticwithapplicationsto independenceresults.............................................. 239 ZiaMovahed Ibn-Sina’santicipationoftheformulasofBuridanandBarcan...... 248 AnandPillay RemarksonalgebraicD-varietiesandthemodeltheoryof differentialfields.................................................. 256 MassoudPourmahdianandFrankWagner AsimplepositiveRobinsontheorywithLSTP(cid:2)=STP............... 270 AlbertVisser Categoriesoftheoriesandinterpretations.......................... 284 PREFACE We are pleased to present the proceedings volume of the invited and con- tributed talks delivered at the Workshop and Conference on Logic, Algebra, andArithmeticthattookplaceOctober18-22,2003attheInstituteforStudies inTheoreticalPhysicsandMathematics(IPM)inTehran,Iran. Themeeting provided a unique occasion for the exchange of ideas and methods in vari- ousfrontiersofresearchinmathematicallogic,andfurtherstrengthenedthe existing bonds of scientific cooperation between Iranian scholars and their colleaguesabroad. The meeting was made possible through the visionary leadership of the director of IPM, Professor M. J. A. Larijani, and the inspiring support of theheadofthemathematicsdivisionatIPM,ProfessorG.B.Khosrovshahi. On behalf of all the participants, we also wish to acknowledge the industry and dedication of the staff at IPM, particularly Mr. M. Rahpeyma, Mr. M. Ashtiani,Mrs.N.Ramezani,andMs.T.Parsa. The papers that appear herein are in most cases revised and expanded versionsofthosethatwereoriginallypresentedatthemeeting. Wearegrateful to the authors for their valuable contributions, patience, and cooperation during the refereeing and revision process. Furthermore, we offer a special note of gratitude to the numerous referees who assisted the authors and the editorsinimprovingthisvolume. Finally,wewouldliketoextendourappreciationtotheASLforpublishing thisvolumeintheLNLseries. TheEditors AliEnayat Washington,DC IrajKalantari Macomb,Illinois MojtabaMoniri Tehran vii WORKSHOP AND CONFERENCE ON LOGIC, ALGEBRA, AND ARITHMETIC TEHRAN, OCTOBER 18–22, 2003 • Organizingcommittee: M.Ardeshir,S.M.Bagheri,A.Enayat,I.Kalantari,M.J.A.Larijani, MojtabaMoniri,MortezaMoniri(Coordinator),andM.Pourmahdian. • Invitedspeakers: L.vandenDries,A.Enayat,Yu.L.Ershov,I.Kalantari,F.-V.Kuhlmann, S.Kuhlmann,A.Pillay,andA.Visser. • Registeredparticipants(inadditiontotheabove): M.Sh. Adib-Soltani Sh.Etemad A.Mohammadian B.Afshari A.Fallahi Sh.Mohsenipour M.Aghaei H.G.Farahani R.Moshtagh-Nazm K.Aghigh M.Ghari Z.Movahed S.Akbari M.Ghasemi L.Nabavi M.Alizadeh K.Ghayoom-Zadeh P.Nasehpour S.M.Amini A.Haghany M.R.Pournaki S.Aqareb-Parast H.Haghighi N.Sadat-Rasooli M.E.Arasteh-Rad M.Hamideh K.Reihani S.M.Ayat M.A.Hojjati H.Sabzrou M.Bargozini S.A.Kalantari P.Safari M.Behzad F.Karimi M.Taherkhani M.R.Changiz M.Kashi H.Talebi A.R.Darabi A.Madanshekaf A.Taromi F.Didehvar M.Mahdavi-Hezavehi M.Tousi K.Divaani-Aazar E.S.Mahmoodian S.Yassemi M.M.Ebrahimi M.Mahmoudi RahimZaare-Nahandi J.S.Eivazloo N.Mani RashidZaare-Nahandi B.Emamizadeh S.H.Masoud M.Zare S.A.Esfahani K.Mehrabadi M.Zekavat • IPMsupportstaff: M.Ashtiani,N.Barati,A.Eslami,M.Hossein-zadehGiv,M.Mashayekhi, T.Parsa,A.A.Rad,M.Rahpeyma,N.Ramezani,andA.Samie.
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