Submission date: 23 July 2020

Abstract:

We prove that if G=(V,E) is an ω-stable (respectively, superstable) graph with χ(G)>ℵ_0 (respectively, 2^{ℵ_0}) then G contains all the finite subgraphs of the shift graph Sh_n(ω) for some n. We prove a variant of this theorem for graphs interpretable in stationary stable theories. Furthermore, if G is ω-stable with U(G) ≤ 2 we prove that n ≤ 2 suffices.

Mathematics Subject Classification:

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Full text arXiv 2007.12139: pdf, ps.