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Complete representations in algebraic logic. (English) Zbl 0893.03025

The authors investigate whether the classes of completely representable Boolean algebras, relation algebras and cylindric algebras form elementary classes, that is, whether there is any set of first-order sentences that characterizes the class, in each case. They prove that a Boolean algebra is completely representable if and only if it is atomic, and neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras are elementary. The results are presented in a game-theoretic framework.

MSC:

03G05 Logical aspects of Boolean algebras
03G15 Cylindric and polyadic algebras; relation algebras
91A80 Applications of game theory
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