A game on partial orderings

by Fuchino and Koppelberg and Shelah. [FKSh:556]
Topology and its Applications, 1996
We study the determinacy of the game G_kappa (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 G_kappa (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 G_kappa (L) for linear orders L .


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