Logic in Tehran

358 Pages·2017·3.886 MB·English

by  Ali Enayat, Iraj Kalantari, Mojtaba Moniri

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
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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.