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Church's Problem asks for the construction of a procedure which, given a logical specification ϕ on sequence pairs, realizes for any input sequence I an output sequence O such that (I, O) satisfies ϕ. McNaughton reduced Church's Problem to a problem about two-player ω-games. Büchi and Landweber gave a solution for Monadic Second-Order Logic of Order (MLO) specifications in terms of finite-state strategies. We consider two natural generalizations of the Church problem to countable ordinals: thedoi:10.4230/lipics.fsttcs.2009.2332 dblp:conf/fsttcs/Rabinovich09 fatcat:awc7tm6ulrgqzk7p3zrq4vhx5y