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

The Hebrew University of Jerusalem

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 - 1 Dec 2023

Keywords

Polarized partition relations
elementary submodels
pcf theory

All Science Journal Classification (ASJC) codes

General Mathematics

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10.36045/j.bbms.230308

Cite this

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title = "An almost strong relation",

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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AU - Garti, Shimon

AU - Villaveces, Andrés

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N2 - 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.

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.

KW - Polarized partition relations

KW - elementary submodels

KW - pcf theory

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U2 - 10.36045/j.bbms.230308

DO - 10.36045/j.bbms.230308

M3 - مقالة

SN - 1370-1444

VL - 30

SP - 456

EP - 467

JO - Bulletin of the Belgian Mathematical Society - Simon Stevin

JF - Bulletin of the Belgian Mathematical Society - Simon Stevin

IS - 4

ER -

An almost strong relation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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