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1、AProblemCourseinMathematicalLogicVersion1.5VolumeIPropositionalandFirst-OrderLogicStefanBilaniukDepartmentofMathematicsTrentUniversityPeterborough,OntarioCanadaK9J7B8E-mailaddress:sbilaniuk@trentu.ca1991MathematicsSubjectClassification.03Keywordsandphrases.propositionallogic,fir
2、st-orderlogicAProblemCourseInMathematicalLogicVolumeI:PropositionalandFirst-OrderLogicVersion1.5Copyright°c1994–1999byStefanBilaniuk.Abstract.Thisisatextforaproblem-orientedundergraduatecourseinmathematicallogic.Itcoversthebasicsofpropositionalandfirst-orderlogicthroughtheSound
3、ness,Completeness,andCompactnessTheorems.VolumeII,Computation,coverstheba-sicsofcomputabilityusingTuringmachinesandrecursivefunc-tions,theIncompletenessTheorems,andcomplexitytheorythroughthePandNP.Informationonavailabalityandtheconditionsunderwhichthisbookmaybeusedandreproduce
4、daregiveninthepreface.ThisbookwastypesetusingLATEX,usingtheAMS-LATEXandAMSFontspackagesoftheAmericanMathematicalSociety.ContentsiiiPrefaceThisbookisintendedtobethebasisforaproblem-orientedfull-yearcourseinmathematicallogicforstudentswithamodicumofmathe-maticalsophistication.Vo
5、lumeIcoversthebasicsofpropositionalandfirst-orderlogicthroughtheSoundness,Completeness,andCompact-nessTheorems,plussomematerialonapplicationsoftheCompactnessTheorem.Itcouldeasilybeusedforaone-semestercourseonthesetopics.VolumeIIcoversthebasicsofcomputabilityusingTuringma-chines
6、andrecursivefunctions,theIncompletenessTheorem,andbasiccomplexitytheory;itcouldalsobeusedasforaone-semestercourseonthesetopics.InkeepingwiththemodifiedMoore-method,thisbooksuppliesdefinitions,problems,andstatementsofresults,alongwithsomeex-planations,examples,andhints.Theintenti
7、sforthestudents,indi-viduallyoringroups,tolearnthematerialbysolvingtheproblemsandprovingtheresultsforthemselves.Besidesconstructivecriticism,itwillprobablybenecessaryfortheinstructortosupplyfurtherhintsordirectthestudentstoothersourcesfromtimetotime.Justhowthistextisusedwill,o
8、fcourse,dependontheinstructorandstudentsinquestion.However,it
