Journal of the Mathematical Society of Japan

Two-cardinal versions of weak compactness: Partitions of triples

Pierre MATET and Toshimichi USUBA

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 1 (2015), 207-230.

Dates
First available in Project Euclid: 22 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1421936551

Digital Object Identifier
doi:10.2969/jmsj/06710207

Mathematical Reviews number (MathSciNet)
MR3304020

Zentralblatt MATH identifier
1330.03080

Subjects
Primary: 03E02: Partition relations 03E55: Large cardinals

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

Citation

MATET, Pierre; USUBA, Toshimichi. Two-cardinal versions of weak compactness: Partitions of triples. J. Math. Soc. Japan 67 (2015), no. 1, 207--230. doi:10.2969/jmsj/06710207. https://projecteuclid.org/euclid.jmsj/1421936551


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