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

Access to Document

10.36045/j.bbms.230308

Cite this

@article{3712f03a0a1549009f0d502ba1331de5,

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.",

keywords = "Polarized partition relations, elementary submodels, pcf theory",

author = "Shimon Garti and Andr{\'e}s Villaveces",

year = "2023",

month = dec,

doi = "10.36045/j.bbms.230308",

language = "אנגלית",

volume = "30",

pages = "456--467",

journal = "Bulletin of the Belgian Mathematical Society - Simon Stevin",

issn = "1370-1444",

publisher = "Belgian Mathematical Society",

number = "4",

}

TY - JOUR

T1 - An almost strong relation

AU - Garti, Shimon

AU - Villaveces, Andrés

PY - 2023/12

Y1 - 2023/12

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

UR - https://www.scopus.com/pages/publications/85182561559

U2 - 10.36045/j.bbms.230308

DO - 10.36045/j.bbms.230308

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85182561559

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

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this