Abstract
M.Sc.
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.