Infinite stable graphs with large chromatic number II

Yatir Halevi; Itay Kaplan; Saharon Shelah

doi:10.4171/JEMS/1352

Infinite stable graphs with large chromatic number II

Yatir Halevi, Itay Kaplan, Saharon Shelah

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

Abstract

We prove a version of the strong Taylor’s conjecture for stable graphs: if G is a stable graph whose chromatic number is strictly greater than ℑ₂(ϰ₀) then G contains all finite subgraphs of Sh_n(ω) and thus has elementary extensions of unbounded chromatic number. This completes the picture from our previous work. The main new model-theoretic ingredient is a generalization of the classical construction of Ehrenfeucht–Mostowski models to an infinitary setting, giving a new characterization of stability.

Original language	English
Pages (from-to)	4585-4614
Number of pages	30
Journal	Journal of the European Mathematical Society
Volume	26
Issue number	12
DOIs	https://doi.org/10.4171/JEMS/1352
State	Published - 1 Jan 2024
Externally published	Yes

Keywords

Chromatic number
EM-models
Taylor’s conjecture
stable graphs

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/JEMS/1352

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abstract = "We prove a version of the strong Taylor{\textquoteright}s conjecture for stable graphs: if G is a stable graph whose chromatic number is strictly greater than ℑ2(ϰ0) then G contains all finite subgraphs of Shn(ω) and thus has elementary extensions of unbounded chromatic number. This completes the picture from our previous work. The main new model-theoretic ingredient is a generalization of the classical construction of Ehrenfeucht–Mostowski models to an infinitary setting, giving a new characterization of stability.",

keywords = "Chromatic number, EM-models, Taylor{\textquoteright}s conjecture, stable graphs",

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AU - Halevi, Yatir

AU - Kaplan, Itay

AU - Shelah, Saharon

PY - 2024/1/1

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N2 - We prove a version of the strong Taylor’s conjecture for stable graphs: if G is a stable graph whose chromatic number is strictly greater than ℑ2(ϰ0) then G contains all finite subgraphs of Shn(ω) and thus has elementary extensions of unbounded chromatic number. This completes the picture from our previous work. The main new model-theoretic ingredient is a generalization of the classical construction of Ehrenfeucht–Mostowski models to an infinitary setting, giving a new characterization of stability.

AB - We prove a version of the strong Taylor’s conjecture for stable graphs: if G is a stable graph whose chromatic number is strictly greater than ℑ2(ϰ0) then G contains all finite subgraphs of Shn(ω) and thus has elementary extensions of unbounded chromatic number. This completes the picture from our previous work. The main new model-theoretic ingredient is a generalization of the classical construction of Ehrenfeucht–Mostowski models to an infinitary setting, giving a new characterization of stability.

KW - Chromatic number

KW - EM-models

KW - Taylor’s conjecture

KW - stable graphs

UR - https://www.scopus.com/pages/publications/85201875719

U2 - 10.4171/JEMS/1352

DO - 10.4171/JEMS/1352

M3 - Article

AN - SCOPUS:85201875719

SN - 1435-9855

VL - 26

SP - 4585

EP - 4614

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 12

ER -

Infinite stable graphs with large chromatic number II

Abstract

Keywords

ASJC Scopus subject areas

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