Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 73, Issue 1 (2008), 238-260.
κ-stationary subsets of 𝒫κ +λ, infinitary games, and distributive laws in Boolean algebras
We characterize the (κ,λ, <μ)-distributive law in Boolean algebras in terms of cut and choose games 𝔖κ<μ(λ), when μ≤κ≤λ and κ<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=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(κ+) but the (κ,∞,κ)-d.l. holds, and, assuming GCH, construct Boolean algebras in which many games are undetermined.
J. Symbolic Logic, Volume 73, Issue 1 (2008), 238-260.
First available in Project Euclid: 16 April 2008
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Dobrinen, Natasha. κ-stationary subsets of 𝒫 κ + λ, infinitary games, and distributive laws in Boolean algebras. J. Symbolic Logic 73 (2008), no. 1, 238--260. doi:10.2178/jsl/1208358752. https://projecteuclid.org/euclid.jsl/1208358752