Abstract
We prove that every abstractly defined game algebra can be represented as an algebra of consistent pairs of monotone outcome relations over a game board. As a corollary we obtain Goranko's result that van Benthem's conjectured axiomatization for equivalent game terms is indeed complete.
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References
Goranko, V.F., ‘The basic algebra of game equivalences’, Studia Logica, 75:221-238, 2003.
Parikh, R., ‘The logic of games and its applications’, Annals of Discrete Mathematics, 24:111-140, 1985.
Pauly, M., ‘Game logic for game theorists’, CWI Technical Report INS-R0017, CWI, Amsterdam, 2000.
Van Benthem, J., Logic in games, Lecture Notes, ILLC, University of Amsterdam, 2000.
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Venema, Y. Representation of Game Algebras. Studia Logica 75, 239–256 (2003). https://doi.org/10.1023/A:1027363028181
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DOI: https://doi.org/10.1023/A:1027363028181