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arXiv · 2103.13931

Infinite Stable Graphs With Large Chromatic Number II

Yatir Halevi·Itay Kaplan·Saharon Shelah
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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 $\beth_2(\aleph_0)$ then $G$ contains all finite subgraphs of Sh$_n(\omega)$ 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.

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BibTeXRIS

Yatir Halevi, Itay Kaplan, Saharon Shelah. 2021-03-25. Infinite Stable Graphs With Large Chromatic Number II. https://arxiv.org/abs/2103.13931

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