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1、AProblemCourseinMathematicalLogicVolumeIIComputabilityandIncompletenessStefanBilaniukDepartmentofMathematicsTrentUniversityPeterborough,OntarioCanadaK9J7B8E-mailaddress:sbilaniuk@trentu.ca1991MathematicsSubjectClassification.03Keywordsandphrases.computability,Turingmachines,recursivefunction
2、s,incompletenessAProblemCourseinMathematicalLogicVolumeII:ComputabilityandIncompletenessVersion1.3Copyright°c1994-1997byStefanBilaniuk.Abstract.ThisistheVolumeIIofatextforaproblem-orientedundergraduatecourseinmathematicallogic.Itcoversthebasicsofcomputability,usingTuringmachinesandrecursive
3、functions,andG¨odel’sIncompletenessTheorem,andcouldbeusedforaone-semestercourseonthesetopics.VolumeI,PropositionalandFirst-OrderLogic,coversthebasicsofthesetopicsthroughtheSound-ness,Completeness,andCompactnessTheorems.Informationonavailabilityandtheconditionsunderwhichthisbookmaybeusedandr
4、eproducedaregiveninthepreface.ThisbookwastypesetusingLATEX,usingtheAMS-LATEXandAMSFontspackagesoftheAmericanMathematicalSociety.ContentsiiiPrefaceThisbookisintendedtobethebasisforaproblem-orientedfull-yearcourseinmathematicallogicforstudentswithamodicumofmathe-maticalsophistication.VolumeII
5、coversthebasicsofcomputability,usingTuringmachinesandrecursivefunctions,andincompleteness.Itcouldbeusedforaone-semestercourseonthesetopics.VolumeIcoversthebasicsofpropositionalandfirst-orderlogicthroughtheSoundness,Completeness,andCompactnessTheorems,plussomema-terialonapplicationsoftheCompa
6、ctnessTheorem;itcouldalsobeusedasforaone-semestercourseonthesetopics.However,partofVolumeII,particularlythechaptersonincompleteness,assumesomefamiliaritywiththebasicsoffirst-orderlogic.InkeepingwiththemodifiedMoore-method,thisbooksuppliesdefinitions,problems,andstatementsofresults,alongwithsom
7、eex-planations,examples,andhints.Theintentisforthestudents,indi-viduallyoringroups,tolearnthematerialbysolvingtheproblemsandprovingtheresultsforthemselves.Besidesconstructivecriticism,itwillprobablybenecessaryfortheinstructortosupplyfurtherhintsordirectt
