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1、GraduateTextsinMathematics53EditorialBoardS.AxlerK.A.RibetForothertitlesinthisseries,gotohttp://www.springer.com/series/136Yu.I.ManinACourseinMathematicalLogicforMathematiciansSecondEditionChaptersI-VIIItranslatedfromtheRussianbyNealKoblitzWithnewchaptersbyBorisZilberandYuriI.ManinAuthor:Contri
2、butor:Yu.I.ManinB.ZilberMax-PlanckInstitutfürMathematikMathematicalInstitute53111BonnUniversityofOxfordGermanyOxfordOX13LBmanin@mpim-bonn.mpg.deUnitedKingdomzilber@maths.ox.ac.ukFirstEditionTranslatedby:NealKoblitzDepartmentofMathematicsUniversityofWashingtonSeattle,WA98195USAkoblitz@math.washi
3、ngton.eduEditorialBoard:S.AxlerK.A.RibetMathematicsDepartmentMathematicsDepartmentSanFranciscoStateUniversityUniversityofCaliforniaatBerkeleySanFrancisco,CA94132Berkeley,CA94720USAUSAaxler@sfsu.eduribet@math.berkeley.eduISSN0072-5285ISBN978-1-4419-0614-4e-ISBN978-1-4419-0615-1DOI10.1007/978-1-4
4、419-0615-1SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2009934521MathematicsSubjectClassification(2000):03-XX,03-01©Secondedition2010byYu.I.Manin©Firstedition1977bySpringerVerlag,NewYork,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthew
5、rittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodol
6、ogynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaperSpringerispartofSpringerScience+Bu
7、sinessMedia(www.springer.com)ToNikita,FedorandMitya,withlovePrefacetotheSecondEdition1.Thefirsteditionofthisbookwaspublishedin1977.Thetexthasbeenwellreceivedandisstillused,althoughithasbeenoutofprintforsometime.Intheinterveningthre
