A Course on Mathematical Logic

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1、KurtGodel(1906–1978)¨S.M.SrivastavaACourseonMathematicalLogic123S.M.SrivastavaIndianStatisticalInstituteKolkataIndiae-mail:smohan@isical.ac.inISBN:978-0-387-76275-3e-ISBN:978-0-387-76277-7DOI:10.1007/978-0-387-76277-7LibraryofCongressControlNumber:2008920049MathematicsSubjectCl

2、assification(2000):03-xx°c2008SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwi

3、threviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,ev

4、eniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedonacid-freepaper987654321springer.comToHAIMANTIContentsPreface.....................................................ix1SyntaxofFirst-OrderLogic............

5、.................11.1First-OrderLanguages................................11.2TermsofaLanguage..................................41.3FormulasofaLanguage...............................61.4First-OrderTheories..................................102SemanticsofFirst-OrderLanguages......

6、..............152.1StructuresofFirst-OrderLanguages....................162.2TruthinaStructure..................................172.3ModelofaTheory....................................192.4EmbeddingsandIsomorphisms.........................203PropositionalLogic....................

7、.................293.1SyntaxofPropositionalLogic..........................303.2SemanticsofPropositionalLogic.......................313.3CompactnessTheoremforPropositionalLogic...........333.4ProofinPropositionalLogic...........................373.5MetatheoremsinPropositionalLog

8、ic....................383.6PostTautologyTheorem.......