The Church Problem for Countable Ordinals
Logic in Computer Science
2015-07-01 v4
Abstract
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.
Cite
@article{arxiv.0811.2198,
title = {The Church Problem for Countable Ordinals},
author = {Alexander Rabinovich},
journal= {arXiv preprint arXiv:0811.2198},
year = {2015}
}