1 results
κ-stationary subsets of
, infinitary games, and distributive laws in Boolean algebras
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- Journal:
- The Journal of Symbolic Logic / Volume 73 / Issue 1 / March 2008
- Published online by Cambridge University Press:
- 12 March 2014, pp. 238-260
- Print publication:
- March 2008
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- Article
- Export citation
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We characterize the (κ, λ, < μ)-distributive law in Boolean algebras in terms of cut and choose games
, 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 in the ground model is preserved by 
. In this vein, we develop the theory of κ-club and κ-stationary subsets of . We also construct Boolean algebras in which Player I wins 
but the (κ, ∞, κ)-d.1. holds, and, assuming GCH, construct Boolean algebras in which many games are undetermined.
, infinitary games, and distributive laws in Boolean algebras
, when 
. In this vein, we develop the theory of 
but the (