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

Einstein Institute of Mathematics

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 - 2024

Bibliographical note

Publisher Copyright:
© 2023 European Mathematical Society.

Keywords

Chromatic number
EM-models
stable graphs
Taylor’s conjecture

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10.4171/JEMS/1352

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Infinite stable graphs with large chromatic number II

Abstract

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Keywords

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