Infinite Games and Uniformization
نویسنده
چکیده
The problem of solvability of infinite games is closely connected with the classical question of uniformization of relations by functions of a given class. We work out this connection and discuss recent results on infinite games that are motivated by the uniformization problem. The fundamental problem in the effective theory of infinite games was posed by Church in 1957 (“Church’s Problem”; see [2, 3]). It refers to two-player games in the sense of Gale and Stewart [6] in which the two players 1 and 2 build up two sequences α = a0a1 . . ., respectively β = b0b1 . . ., where ai, bi belong to a finite alphabet Σ. Player 1 picks a0, then Player 2 picks b0, then Player 1 picks a1, and so forth in alternation. A play is an ω-word over Σ × Σ of the form (
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