# Sh:556

• Fuchino, S., Koppelberg, S., & Shelah, S. (1996). A game on partial orderings. Topology Appl., 74(1-3), 141–148.
• 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.
• published version (8p)
Bib entry
@article{Sh:556,
author = {Fuchino, Saka{\'e} and Koppelberg, Sabine and Shelah, Saharon},
title = {{A game on partial orderings}},
booktitle = {{Proceedings of the International Conference on Set-theoretic Topology and its Applications (Matsuyama, 1994)}},
journal = {Topology Appl.},
fjournal = {Topology and its Applications},
volume = {74},
number = {1-3},
year = {1996},
pages = {141--148},
issn = {0166-8641},
doi = {10.1016/S0166-8641(96)00051-X},
mrclass = {03E05 (90D44)},
mrnumber = {1425933},
mrreviewer = {Carlos A. Di Prisco},
doi = {10.1016/S0166-8641(96)00051-X},
note = {\href{https://arxiv.org/abs/math/9505212}{arXiv: math/9505212}},
arxiv_number = {math/9505212}
}