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January, 2015 Two-cardinal versions of weak compactness: Partitions of triples
Pierre MATET, Toshimichi USUBA
J. Math. Soc. Japan 67(1): 207-230 (January, 2015). DOI: 10.2969/jmsj/06710207


Let κ be a regular uncountable cardinal, and λ be a cardinal greater than κ. Our main result asserts that if (λ< κ)<(λ< κ) = λ< κ, then (pκ, λ(NInκ, λ< κ))+ $\longrightarrow$ ((NSκ, λ[λ]< κ)+, NSκ, λs+)3 and (pκ, λ(NAInκ, λ< κ))+ $\longrightarrow$ (NSκ, λs+)3, where NSκ, λs (respectively, NSκ, λ[λ]< κ) denotes the smallest seminormal (respectively, strongly normal) ideal on Pκ (λ), NInκ, λ< κ (respectively, NAInκ, λ< κ) denotes the ideal of non-ineffable (respectively, non-almost ineffable) subsets of Pκ< κ), and pκ, λ: Pκ< κ) → Pκ (λ) is defined by pκ, λ(x) = x ∩ λ.


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Pierre MATET. Toshimichi USUBA. "Two-cardinal versions of weak compactness: Partitions of triples." J. Math. Soc. Japan 67 (1) 207 - 230, January, 2015.


Published: January, 2015
First available in Project Euclid: 22 January 2015

zbMATH: 1330.03080
MathSciNet: MR3304020
Digital Object Identifier: 10.2969/jmsj/06710207

Primary: 03E02 , 03E55

Keywords: $P_\kappa(\lambda)$ , partition relation , weakly compact cardinal

Rights: Copyright © 2015 Mathematical Society of Japan


Vol.67 • No. 1 • January, 2015
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