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Two-cardinal diamond and games of uncountable length

Abstract : Let μ,κ and λ be three uncountable cardinals such that μ=cf(μ)<κ=cf(κ)<λ. The game ideal NGμκ,λ is a normal ideal on Pκ(λ) defined using games of length μ. We show that if 2(κμ)≤λ and there are no (fairly) large cardinals in an inner model, then the diamond principle ♢κ,λ[NGμκ,λ] holds. We also show that if ♢κ(S) holds, where S is a stationary subset of κ, then ♢κ,λ({a∈Pκ(λ):a∩κ∈S}) holds.
Keywords : Pκ(λ) ♢κ λ Games
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https://hal-normandie-univ.archives-ouvertes.fr/hal-02145588
Contributor : Pierre Matet <>
Submitted on : Monday, June 3, 2019 - 10:27:00 AM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM

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Pierre Matet. Two-cardinal diamond and games of uncountable length. Archive for Mathematical Logic, Springer Verlag, 2015, 54 (3-4), pp.395-412. ⟨10.1007/s00153-014-0415-6⟩. ⟨hal-02145588⟩

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