A game on partial orderings
Logic
2016-09-06 v1
Abstract
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 .
Keywords
Cite
@article{arxiv.math/9505212,
title = {A game on partial orderings},
author = {Sakaé Fuchino and Sabine Koppelberg and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9505212},
year = {2016}
}