Solving Infinite Games in the Baire Space

Infinite games (in the form of Gale-Stewart games) are studied where a play is a se- quence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space ωω . We consider such games defined by a natural kind of parity au- tomata over the alphabet N, called N-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical Büchi-Landweber Theorem (for finite-state games in the Cantor space 2ω) holds again for the present games: A game defined by a deterministic parity N-MSO-automaton is deter- mined, the winner can be computed, and an N-MSO-transducer realizing a winning strategy for the winner can be constructed.