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1、AProblemCourseinMathematicalLogicVersion1.5VolumeIPropositionalandFirst-OrderLogicStefanBilaniukDepartmentofMathematicsTrentUniversityPeterborough,OntarioCanadaK9J7B8E-mailaddress:sbilaniuk@trentu.ca1991MathematicsSubjectClassification.03Keywordsandphrases
2、.propositionallogic,first-orderlogicAProblemCourseInMathematicalLogicVolumeI:PropositionalandFirst-OrderLogicVersion1.5Copyright°c1994–1999byStefanBilaniuk.Abstract.Thisisatextforaproblem-orientedundergraduatecourseinmathematicallogic.Itcoversthebasicsofpr
3、opositionalandfirst-orderlogicthroughtheSoundness,Completeness,andCompactnessTheorems.VolumeII,Computation,coverstheba-sicsofcomputabilityusingTuringmachinesandrecursivefunc-tions,theIncompletenessTheorems,andcomplexitytheorythroughthePandNP.Informationona
4、vailabalityandtheconditionsunderwhichthisbookmaybeusedandreproducedaregiveninthepreface.ThisbookwastypesetusingLATEX,usingtheAMS-LATEXandAMSFontspackagesoftheAmericanMathematicalSociety.ContentsiiiPrefaceThisbookisintendedtobethebasisforaproblem-orientedf
5、ull-yearcourseinmathematicallogicforstudentswithamodicumofmathe-maticalsophistication.VolumeIcoversthebasicsofpropositionalandfirst-orderlogicthroughtheSoundness,Completeness,andCompact-nessTheorems,plussomematerialonapplicationsoftheCompactnessTheorem.Itc
6、ouldeasilybeusedforaone-semestercourseonthesetopics.VolumeIIcoversthebasicsofcomputabilityusingTuringma-chinesandrecursivefunctions,theIncompletenessTheorem,andbasiccomplexitytheory;itcouldalsobeusedasforaone-semestercourseonthesetopics.Inkeepingwiththemo
7、difiedMoore-method,thisbooksuppliesdefinitions,problems,andstatementsofresults,alongwithsomeex-planations,examples,andhints.Theintentisforthestudents,indi-viduallyoringroups,tolearnthematerialbysolvingtheproblemsandprovingtheresultsforthemselves.Besidescons
8、tructivecriticism,itwillprobablybenecessaryfortheinstructortosupplyfurtherhintsordirectthestudentstoothersourcesfromtimetotime.Justhowthistextisusedwill,ofcourse,dependontheinstructorandstudentsinquestion.However,it
