Fundamentals of Mathematical Logic

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1、FUNDAMENTALSOFATHEATICALOGICF1LIFvLE'FvL/,-yF/LPETERG.HINMANFundamentalsofMathematicalLogicPeterG.HinmanUniversityofMichiganAKPetersWellesley,MassachusettsEditorial,Sales,andCustomerServiceOfficeAKPeters,Ltd.888WorcesterStreet,Suite230Wellesley,MA02482www.akpe

2、ters.comCopyright©2005byAKPeters,Ltd.Allrightsreserved.Nopartofthematerialprotectedbythiscopyrightnoticemaybereproducedorutilizedinanyform,electronicormechani•cal,includingphotocopying,recording,orbyanyinformationstorageandretrievalsystem,withoutwrittenpermission

3、fromthecopyrightowner.LibraryofCongressCataloging-in-PublicationDataHinman,PeterG.Fundamentalsofmathematicallogic/PeterG.Hinman.p.cm.Includesbibliographicalreferencesandindexes.ISBN1-56881-262-01.Logic,Symbolicandmathematical.2.Modeltheory.3.Settheory.4.Recursion

4、theory.I.Title.QA9.H5272005511.3--dc222005050968PrintedinIndia090807060510987654321ContentsPreface...xiIntroduction11.PropositionalLogicandOtherFundamentals.131.1.Thepropositionallanguage...131.2.Inductionandrecursion20Induction.20Recursion.251.3.Propositionalsem

5、antics321.4.Propositionaltheories..41Generalproperties42Compactness.........471.5.Decidabilityandeffectiveenumerability541.6.Otherconstructions..63Notionsofconsistency....63Ultraproducts.671.7.TopologyandBooleanalgebra72Topology....73Booleanalgebra74viiiContents2

6、.First-OrderLogic832.1.Syntaxandsemanticsoffirst-orderlanguages.832.2.Basicsemantics.96Substitution........1052.3.Structures........114Isomorphismandequivalence115Substructures119Productsandchains....1302.4.Theories........139Thelanguageofequality..149Denselinear

7、orderings.1542.5.Arithmetic..........1602.6.Changinglanguages.173Interpretations...1863.CompletenessandCompactness1933.1.Countablecompactness....1943.2.Countablecompleteness....2043.3.Otherconstructions..216Notionsofconsistency216Ultraproducts224Booleanalgebra228

8、3.4.Uncountablelanguagesandstructures.2363.5.Applicationsofcompactness....2493.6.Higher-orderlogic.....276Monadicsecond-orderlogic..2763.7.Infinitarylogic.....