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1、H.-D.EbbinghausJ.FlumW.ThomasMathematicalLogicSpringer-VerlagNewYorkBerlinHeidelbergTokyoH.-D.EbbinghausW.ThomasJ.FlumLehrstuhlfiirInformatik11MathematischesInstitutRWTHAachenUniversitatFreiburgBiichel29-31Albertstrasse23b5100Aachen7800FreiburgFederalRepublicofFederalRepublicof
2、GermanyGermanyEditorialBoardP.R.HalmosF.W.GehringDepartmentofMathematicsDepartmentofMathematicsIndianaUniversity,UniversityofMichiganBloomington,IN47405AnnArbor,MI48109U.S.A.U.S.A.TranslatedfromEinjlihr~myindiemuthc~matischeLogik,publishedbyWissenschaftlicheBuchgesellschaft.Dar
3、mstadt.byAnnS.Ferebee,Kohlweg12,D-6240Konigstein4,FederalRepublicofGermany.-AMSSubjectClassification(1980):03-01LibraryofCongressCataloginginPublicationDataEbbinghaus,Heinz-Dieter,1939athematicallogic.(Undergraduatetextsinmathematics)Translationof:EinfiihrungindiemathematischeL
4、ogik,Bibliography:p.Includesindex.1.Logic,Symbolicandmathematical.I.Flum,Jorg.11.Thomas,Wolfgang.111.Title.IV.Series.QA9.E22131984511.383-20060With1Illustration@1984bySpringer-VerlagNewYorkInc.Allrightsreserved.Nopartofthisbookmaybetranslatedorreproducedinanyformwithoutwrittenp
5、ermissionfromSpringer-Verlag,175FifthAvenue,.NewYork,NewYork10010,U.S.A.TypesetbyCompositionHouseLtd.,Salisbury,England.PrintedandboundbyR.R.Donnelley&Sons,Harrisonburg,VirginiaPrintedintheUnitedStatesofAmerica.ISBN0-387-90895-1Springer-VerlagNewYorkBerlinHeidelbergTokyoISBN3-5
6、40-90895-1Springer-VerlagBerlinHeidelbergNewYorkTokyoPrefacerSomeofthecentralquestionsofmathematicallogicare:Whatisamathematicalproof?Howcanproofsbejustified?Aretherelimitationstoprovability?Towhatextentcanmachinescarryoutmathematicalproofs?Onlyinthiscenturyhastherebeensuccessi
7、nobtainingsubstantialandsatisfactoryanswers,themostpleasingofwhichisgivenbyGodel'scompletenesstheorem:Itispossibletoexhibit(intheframeworkoffirst-orderlanguages)asimplelistofinferenceruleswhichsufficestocarryoutallmathematicalproofs."Negative"results,however,appearinGodel'sinco
8、mpletenesstheorems.Theyshow,forexample,thatitisimpossi
