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March 2008 κ-stationary subsets of 𝒫κ +λ, infinitary games, and distributive laws in Boolean algebras
Natasha Dobrinen
J. Symbolic Logic 73(1): 238-260 (March 2008). DOI: 10.2178/jsl/1208358752

Abstract

We characterize the (κ,λ, <μ)-distributive law in Boolean algebras in terms of cut and choose games 𝔖κ(λ), when μ≤κ≤λ and κ=κ. This builds on previous work to yield game-theoretic characterizations of distributive laws for almost all triples of cardinals κ,λ,μ with μ≤λ, under GCH. In the case when μ≤κ≤λ and κ=κ, we show that it is necessary to consider whether the κ-stationarity of 𝒫κ+λ in the ground model is preserved by 𝔹. In this vein, we develop the theory of κ-club and κ-stationary subsets of 𝒫κ+λ. We also construct Boolean algebras in which Player I wins 𝔖κκ+) but the (κ,∞,κ)-d.l. holds, and, assuming GCH, construct Boolean algebras in which many games are undetermined.

Citation

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Natasha Dobrinen. "κ-stationary subsets of 𝒫κ +λ, infinitary games, and distributive laws in Boolean algebras." J. Symbolic Logic 73 (1) 238 - 260, March 2008. https://doi.org/10.2178/jsl/1208358752

Information

Published: March 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1142.03031
MathSciNet: MR2387942
Digital Object Identifier: 10.2178/jsl/1208358752

Subjects:
Primary: 03E05, 03E40, 03G05, 06E10

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 1 • March 2008
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