Mathematical Logic

Undergraduatestudentswithnopriorclassroominstructioninmathematicallogicwillbenefitfromthisevenhandedmultiparttext.Itbeginswithanelementarybutthoroughoverviewofmathematicallogicoffirstorder.Thetreatmentextendsbeyondasinglemethodofformulatinglogictoofferinstructioninavarietyoftechniques:modeltheory(truthtables),Hilbert-typeprooftheory,andprooftheoryhandledthroughderivedrules.Thesecondpartsupplementsthepreviouslydiscussedmaterialandintroducessomeofthenewerideasandthemoreprofoundresultsoftwentieth-centurylogicalresearch.Subsequentchaptersexplorethestudyofformalnumbertheory,withsurveysofthefamousincompletenessandundecidabilityresultsofGodel,Church,Turing,andothers.Theemphasisinthefinalchapterrevertstologic,withexaminationsofGodel'scompletenesstheorem,Gentzen'stheorem,Skolem'sparadoxandnonstandardmodelsofarithmetic,andothertheorems.Theauthor,StephenColeKleene,wasCyrusC.MacDuffeeProfessorofMathematicsattheUniversityofWisconsin,Madison.Preface.Bibliography.TheoremandLemmaNumbers:Pages.ListofPostulates.SymbolsandNotations.