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1、LogicandComputationLecturenotesJeremyAvigadAssistantProfessor,PhilosophyCarnegieMellonUniversityVersion:January2002PrefaceThisdocumentcomprisesasetoflecturenotesthatIpreparedinthefallof1998,whileteachingacoursecalledLogicandComputationinthePhiloso-phyDepartmentatCarnegieMellonUniversity.Idistribu
2、tedthesenotestotheclassandthenfollowedthemalmostwordforword,inthehopesthatdoingsowouldenablestudentstopaymoreattentiontothecontentsofthelectures,andfreethemfromthedrudgeryoftranscription.Thenotesweredesignedtosupplementthetextbookratherthantoreplaceit,andsotheyaremorewordyandinformalthanmosttextb
3、ooksinsomeplaces,andlessdetailedinothers.LogicandComputationiscross-listedasanintroductorygraduatecourse(80-610)andasanadvancedcourseforundergraduates(80-310).Moststudentswereinthephilosophydepartment,ineithertheundergraduatemajorinLogicandComputation,themasters’programofthesamename,orthePh.D.pro
4、graminLogic,Computation,andMethodology.Therewasalsoacontingencyofstudentsfromcomputerscience,andasmalleronefrommathematics(whichmaintainsitsownseriesoflogiccourses).Withthisinmind,Itriedtopresentthecourseasarigorousintroductiontomathematicallogic,whichlentsomeattentiontophilosophicalcontextandcom
5、putationalrelevance,butdidnotrequireagooddealofmathematicalbackground.Asprerequisites(describedinmoredetailinChapter1),Irequiredsomefamiliaritywithfirst-orderlogic,andsomebackgroundinreadingandwritingmathematicalproofs.ForatextbookIusedDirkvanDalen’sLogicandStructure,whichIlikeverymuch,eventhoughi
6、tiswrittenforamoremathematicalaudience.AtvariouspointsinthesemesterIalsocirculatedafewpagestakenfromEn-derton’sMathematicalLogic,and,forhistoricalperspective,supplementarywritingsfromTarski,Russell,etc.Ihavecontinuedtousethenotesinsubsequentyears,andIhavemadesomeminoradditionsandcorrectionsalongt
7、heway.Butusethesenoteswithcaution:theyarenotofpublicationquality,andthereareboundtobeiiimanyerrorsandinconsistencies.Pleaseletmeknowifyoufindthesenotesusefulinanyway.Iwillbehappytomakeweeklyhomeworkassignmentsandotherha
