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1、UNDECIDABLETHEORIESBYALFREDTARSKIProfessorofMathematics,UniversityofCalifornia,BerkeleyINCOLLABORATIONWITHANDRZEJMOSTOWSKIProfessorofMathematics,UniversityofWarsawANDRAPHAELMROBINSONProfessorofMathematics,UniversityofCalifornia,BerkeleyI1971NORTH-HOLLANDPUBLISHINGCOMPANYA
2、MSTERDAM©North-HollandPublishingCompany-1953Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorother-wise,withoutthepriorpermissionofthecopyrightownerISBN:0720
3、422469Firstedition1953Secondprinting1968Thirdprinting1971PRINTBDINTBBNKTIIBltLAM>SPREFACEThismonographconsistsofthreepapers:Ageneralmethodinproofsofundecidability,Undecidabilityandessentialundecidabilityinarithmetic,Undecidabilityoftheelementarytheoryofgroups.Whilethefirs
4、tandthethirdpapershavebeenwrittenbytheundersignedalone,thesecondpaperisajointworkofA.Mostowski,R.M.Robinson,andtheundersigned.ThethreepapersarereferredtothroughoutthemonographbyRomannumeralsI,II,III.TheintroductiontopaperIisthoughtofasanintroductiontothewholeworkandgivesa
5、nideaofthescopeoftheproblemsdiscussedandtheresultsobtained.Thenotationsandsymbolicconventionsintroducedatanyplaceofthemonographareappliedinthewholesubsequentdiscussion.Theworkcontainsresultsobtainedoveralongperiodoftime,1938-1952.ThefirstdraftofpaperIIwaspreparedbyMostows
6、kiin1949andcontainedexclusivelyresultsfoundbyhimandTarskiinthepre-warperiod.However,itspublicationwaspostponedandthetextwasconsiderablymodified,soastoembodytheresultsandsimplificationssubsequentlyobtainedbyRobinsonandpartlybyTarski;thefinaldraftwaswrittenjointlybythesetwo
7、authorsin1951-52.Theothertwopaperswerepreparedforpublicationduringthesameperiod.Itwasoriginallyplannedtopublishtheworkasaseriesofconnectedpapersinsomeregularmathematicalperiodical.How-ever,theEditorsoftheseriesStudiesinLogicfoundthematerialintegratedenoughtoappearasasepar
8、atevolumeinthisseries;theirofferwasacceptedwithappreciation.Alargepartofthetechnicalworkonthemon
