Abstract
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. Bibliography: 8 titles.
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