A game theoretic property of Boolean algebras1)

Publisher Summary This chapter introduces an infinite game played on a Boolean algebra, and investigates the properties of Boolean algebras defined in terms of existence of winning strategies in the game. The chapter demonstrates that the properties are closely related to distributivity laws for Boolean algebras. The chapter illustrates an example of a Boolean algebra for which the game presented in the chapter is not determined. The chapter defines the game GB for Boolean algebras, to compare the existence of strategies with standard Boolean algebraic properties.

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