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Game-theoretic methods in logic

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dc.contributor.advisor Prof. V.F. Goranko en_US
dc.contributor.author Dorfling, Michael Jacobus
dc.date.accessioned 2012-08-17T08:55:50Z
dc.date.available 2012-08-17T08:55:50Z
dc.date.issued 2012-08-17
dc.date.submitted 1999-02
dc.identifier.uri http://hdl.handle.net/10210/6086
dc.description M.Sc. en_US
dc.description.abstract The aim of the thesis is to develop game-theoretic techniques for dealing with common problems in model theory, mainly that of showing logical equivalence between structures, and to illustrate the effectiveness of the game-theoretic approach by means of examples. Chapter 1 gives the basic definitions regarding first-order logic and structures. Chapter 2 introduces Ehrenfeucht's game and the associated characterization of elementary equivalence. We give some applications to definability and completeness and we show how the restrictions in Ehrenfeucht's theorem can be circumvented. In Chapter 3 we obtain extensions of Ehrenfeucht's theorem for monadic second-order logic, infinitary logic, logics with cardinality quantifiers and first-order logic with a bounded number of variables. Chapter 4 discusses modal logic and the game-theoretic counterparts of bisimulation and bounded bisimulation. We also obtain bisimulations as fixed points of certain operators. In Chapter 5 we discuss a general framework in which all our games fit and we briefly mention a game-theoretic approach to forcing and game-theoretic semantics. en_US
dc.language.iso en en_US
dc.subject Game theory en_US
dc.subject Logic, Symbolic and mathematical en_US
dc.subject Logic en_US
dc.title Game-theoretic methods in logic en_US
dc.type Mini-Dissertation en_US

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