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1、DirkvanDalenLogicandStructureFourthEditionABCDirkvanDalenDepartmentofPhilosophyUtrechtUniversityHeidelberglaan8P.O.Box801263508TCUtrechtTheNetherlandsdirk.vandalen@phil.uu.nlCorrected2ndprinting2008ISBN978-3-540-20879-2LibraryofCongressControlNumber:2008929906MathematicsSubjectClassificati
2、on(2000):03-01(textbook);03B15,03F05,03C07c2004,1994,1983,1980Springer-VerlagBerlinHeidelbergThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broad-casting,reproduc
3、tiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCop
4、yrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantpro-tectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:ErichKirchner,HeidelbergPrintedonacid-free
5、paper987654321springer.comPrefaceLogicappearsina‘sacred’andina‘profane’form;thesacredformisdomi-nantinprooftheory,theprofaneforminmodeltheory.Thephenomenonisnotunfamiliar,oneobservesthisdichotomyalsoinotherareas,e.g.setthe-oryandrecursiontheory.Someearlycatastrophies,suchasthediscoveryoft
6、hesettheoreticalparadoxes(Cantor,Russell),orthedefinabilityparadoxes(Richard,Berry),makeustreatasubjectforsometimewiththeutmostaweanddiffidence.Soonerorlater,however,peoplestarttotreatthemat-terinamorefreeandeasyway.Beingraisedinthe‘sacred’tradition,myfirstencounterwiththeprofanetraditionwass
7、omethinglikeacultureshock.HartleyRogersintroducedmetoamorerelaxedworldoflogicbyhisexampleofteachingrecursiontheorytomathematiciansasifitwerejustanordinarycoursein,say,linearalgebraoralgebraictopology.InthecourseoftimeIhavecometoacceptthisviewpointasthedidacticallyso
