A game on partial orderings

Details A game on partial orderings A game on partial orderings

1995-05-15

arxiv.org/abs/math/9505212v1

Topology Appl. 74 (1996), 141-148

Mathematics

Logic

Scientific paper

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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