Complicated colorings, revisited

Assaf Rinot; Jing Zhang

doi:10.1016/j.apal.2022.103243

Complicated colorings, revisited

Assaf Rinot, Jing Zhang

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

2 Scopus citations

Abstract

In a paper from 1997, Shelah asked whether Pr₁(λ⁺,λ⁺,λ⁺,λ) holds for every inaccessible cardinal λ. Here, we prove that an affirmative answer follows from □(λ⁺). Furthermore, we establish that for every pair χ<κ of regular uncountable cardinals, □(κ) implies Pr₁(κ,κ,κ,χ).

Original language	English
Article number	103243
Journal	Annals of Pure and Applied Logic
Volume	174
Issue number	4
DOIs	https://doi.org/10.1016/j.apal.2022.103243
State	Published - 1 Apr 2023
Externally published	Yes

Keywords

Square
Strong colorings
Walks on ordinals

ASJC Scopus subject areas

Logic

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10.1016/j.apal.2022.103243

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title = "Complicated colorings, revisited",

abstract = "In a paper from 1997, Shelah asked whether Pr1(λ+,λ+,λ+,λ) holds for every inaccessible cardinal λ. Here, we prove that an affirmative answer follows from □(λ+). Furthermore, we establish that for every pair χ<κ of regular uncountable cardinals, □(κ) implies Pr1(κ,κ,κ,χ).",

keywords = "Square, Strong colorings, Walks on ordinals",

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AU - Rinot, Assaf

AU - Zhang, Jing

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AB - In a paper from 1997, Shelah asked whether Pr1(λ+,λ+,λ+,λ) holds for every inaccessible cardinal λ. Here, we prove that an affirmative answer follows from □(λ+). Furthermore, we establish that for every pair χ<κ of regular uncountable cardinals, □(κ) implies Pr1(κ,κ,κ,χ).

KW - Square

KW - Strong colorings

KW - Walks on ordinals

UR - https://www.scopus.com/pages/publications/85147364561

U2 - 10.1016/j.apal.2022.103243

DO - 10.1016/j.apal.2022.103243

M3 - Article

AN - SCOPUS:85147364561

SN - 0168-0072

VL - 174

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 4

M1 - 103243

ER -

Complicated colorings, revisited

Abstract

Keywords

ASJC Scopus subject areas

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