An almost strong relation

Shimon Garti; Andrés Villaveces

doi:10.36045/j.bbms.230308

An almost strong relation

Shimon Garti, Andrés Villaveces

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let µ be a strong limit singular cardinal. We prove that if 2^µ > µ⁺ then the almost strong polarized partition relation (^µ_µ⁺) → (_µ^τ)_θ for every ordinal τ < µ⁺ and for every θ < cf(µ). We obtain an optimal positive relation under 2^µ = µ⁺, as after collapsing 2^µ to µ⁺ this positive relation is preserved.

Original language	English
Pages (from-to)	456-467
Number of pages	12
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	30
Issue number	4
DOIs	https://doi.org/10.36045/j.bbms.230308
State	Published - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 Belgian Mathematical Society. All rights reserved.

Keywords

Polarized partition relations
elementary submodels
pcf theory

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10.36045/j.bbms.230308

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abstract = "Let µ be a strong limit singular cardinal. We prove that if 2µ > µ+ then the almost strong polarized partition relation (µµ+) → (µτ)θ for every ordinal τ < µ+ and for every θ < cf(µ). We obtain an optimal positive relation under 2µ = µ+, as after collapsing 2µ to µ+ this positive relation is preserved.",

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AB - Let µ be a strong limit singular cardinal. We prove that if 2µ > µ+ then the almost strong polarized partition relation (µµ+) → (µτ)θ for every ordinal τ < µ+ and for every θ < cf(µ). We obtain an optimal positive relation under 2µ = µ+, as after collapsing 2µ to µ+ this positive relation is preserved.

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KW - elementary submodels

KW - pcf theory

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An almost strong relation

Abstract

Bibliographical note

Keywords

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