可数序数的Church问题
The Church Problem for Countable Ordinals
摘要：
Buchi和Landweber的一个基本定理表明Church综合问题是可计算的。Buchi和Landweber将教会问题简化为关于博弈的问题，并将这种博弈的确定性作为证明其可计算性的主要工具之一。我们认为一个自然的推广教堂问题可数序数和调查游戏的任意可数长度。我们证明了Bu}chi和Landweber定理的决定性和可判定性部分对所有可数序数都成立，并且它的完全推广对所有序数< ω\^ω都成立。
英文摘要：
A fundamental theorem of Buchi and Landweber shows that the Church synthesis problem is computable. Buchi and Landweber reduced the Church Problem to problems about ω-games and used the determinacy of such games as one of the main tools to show its computability. We consider a natural generalization of the Church problem to countable ordinals and investigate games of arbitrary countable length. We prove that determinacy and decidability parts of the Bu}chi and Landweber theorem hold for all countable ordinals and that its full extension holds for all ordinals < ω\^ω.
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