The Church Problem for Countable Ordinals

Details The Church Problem for Countable Ordinals The Church Problem for Countable Ordinals

2008-11-13

arxiv.org/abs/0811.2198v4

LMCS 5 (2:5) 2009

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-5(2:5)2009

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 < \omega\^\omega.

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