A game on partial orderings
Abstract
We study the determinacy of the game Gkappa (A) introduced in [FKSh:549] for uncountable regular kappa and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that Gkappa (A) is undetermined. For the class of linear orders, the existence of such A depends on the size of kappa< kappa. In particular we obtain a characterization of kappa< kappa= kappa in terms of determinacy of the game Gkappa (L) for linear orders L .
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