Infinite Stable Graphs With Large Chromatic Number II
Logic
2021-03-26 v1 Combinatorics
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 Sh 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
@article{arxiv.2103.13931,
title = {Infinite Stable Graphs With Large Chromatic Number II},
author = {Yatir Halevi and Itay Kaplan and Saharon Shelah},
journal= {arXiv preprint arXiv:2103.13931},
year = {2021}
}