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1、GraduateTextsinMathematics53EditorialBoardS.AxlerK.A.RibetForothertitlesinthisseries,gotohttp://www.springer.com/series/136Yu.I.ManinACourseinMathematicalLogicforMathematiciansSecondEditionChaptersI-VIIItranslatedfromtheRussianbyNealKoblitzWithnewchaptersbyBorisZilberandYuriI.ManinAu
2、thor:Contributor:Yu.I.ManinB.ZilberMax-PlanckInstitutfürMathematikMathematicalInstitute53111BonnUniversityofOxfordGermanyOxfordOX13LBmanin@mpim-bonn.mpg.deUnitedKingdomzilber@maths.ox.ac.ukFirstEditionTranslatedby:NealKoblitzDepartmentofMathematicsUniversityofWashingtonSeattle,WA9819
3、5USAkoblitz@math.washington.eduEditorialBoard:S.AxlerK.A.RibetMathematicsDepartmentMathematicsDepartmentSanFranciscoStateUniversityUniversityofCaliforniaatBerkeleySanFrancisco,CA94132Berkeley,CA94720USAUSAaxler@sfsu.eduribet@math.berkeley.eduISSN0072-5285ISBN978-1-4419-0614-4e-ISBN97
4、8-1-4419-0615-1DOI10.1007/978-1-4419-0615-1SpringerNewYorkDordrechtHeidelbergLondonLibraryofCongressControlNumber:2009934521MathematicsSubjectClassification(2000):03-XX,03-01©Secondedition2010byYu.I.Manin©Firstedition1977bySpringerVerlag,NewYork,Inc.Allrightsreserved.Thisworkmaynotbe
5、translatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadap
6、tation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprieta
7、ryrights.Printedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)ToNikita,FedorandMitya,withlovePrefacetotheSecondEdition1.Thefirsteditionofthisbookwaspublishedin1977.Thetexthasbeenwellreceivedandisstillused,althoughithasbeenoutofprintforsometime.Intheint
8、erveningthre
