The Banach–Mazur game

The Banach–Mazur game is investigated on the set of all general recursive functions. The concept of the category of a set of general recursive functions is introduced. This concept is used to formulate and prove necessary and sufficient conditions for the existence of a winning strategy for one of the players in the Banach–Mazur game, the conditions in question being analogous to the theorems of Banach for the Banach–Mazur game on the set of real numbers. The concept of the measure of a set of general recursive functions is also introduced, and the relationship between this concept and the one of category is given.
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