A game on partial orderings

Sakaé Fuchino; Sabine Koppelberg; Saharon Shelah

doi:10.1016/s0166-8641(96)00051-x

A game on partial orderings

Sakaé Fuchino^*, Sabine Koppelberg, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study the determinacy of the game G_κ(A) introduced in Fuchino, Koppelberg and Shelah (to appear) for uncountable regular κ and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that G_κ(A) is undetermined. For the class of linear orders, the existence of such A depends on the size of κ^<κ. In particular we obtain a characterization of κ^<κ = κ in terms of determinacy of the game G_κ(L) for linear orders L.

Original language	English
Pages (from-to)	141-148
Number of pages	8
Journal	Topology and its Applications
Volume	74
Issue number	1-3
DOIs	https://doi.org/10.1016/s0166-8641(96)00051-x
State	Published - 1996

Keywords

Boolean algebras
Freese-Nation property
Games
Linear orders
Trees

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10.1016/s0166-8641(96)00051-x

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abstract = "We study the determinacy of the game Gκ(A) introduced in Fuchino, Koppelberg and Shelah (to appear) for uncountable regular κ and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that Gκ(A) is undetermined. For the class of linear orders, the existence of such A depends on the size of κ<κ. In particular we obtain a characterization of κ<κ = κ in terms of determinacy of the game Gκ(L) for linear orders L.",

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AU - Koppelberg, Sabine

AU - Shelah, Saharon

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AB - We study the determinacy of the game Gκ(A) introduced in Fuchino, Koppelberg and Shelah (to appear) for uncountable regular κ and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that Gκ(A) is undetermined. For the class of linear orders, the existence of such A depends on the size of κ<κ. In particular we obtain a characterization of κ<κ = κ in terms of determinacy of the game Gκ(L) for linear orders L.

KW - Boolean algebras

KW - Freese-Nation property

KW - Games

KW - Linear orders

KW - Trees

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JO - Topology and its Applications

JF - Topology and its Applications

IS - 1-3

ER -

A game on partial orderings

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Keywords

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