Infinite stable graphs with large chromatic number II

  • Yatir Halevi

    Haifa University, Israel
  • Itay Kaplan

    The Hebrew University of Jerusalem, Israel
  • Saharon Shelah

    The Hebrew University of Jerusalem, Israel
Infinite stable graphs with large chromatic number II cover
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Abstract

We prove a version of the strong Taylor’s conjecture for stable graphs: if is a stable graph whose chromatic number is strictly greater than then contains all finite subgraphs of 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.

Cite this article

Yatir Halevi, Itay Kaplan, Saharon Shelah, Infinite stable graphs with large chromatic number II. J. Eur. Math. Soc. 26 (2024), no. 12, pp. 4585–4614

DOI 10.4171/JEMS/1352