Is Ramsey's theorem omega-automatic?
Logic in Computer Science
2010-02-03 v2 Discrete Mathematics
Formal Languages and Automata Theory
Abstract
We study the existence of infinite cliques in omega-automatic (hyper-)graphs. It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as for automatic graphs. More specifically, we show that every uncountable omega-automatic graph contains an uncountable co-context-free clique or anticlique, but not necessarily a context-free (let alone regular) clique or anticlique. We also show that uncountable omega-automatic ternary hypergraphs need not have uncountable cliques or anticliques at all.
Cite
@article{arxiv.0912.2625,
title = {Is Ramsey's theorem omega-automatic?},
author = {Dietrich Kuske},
journal= {arXiv preprint arXiv:0912.2625},
year = {2010}
}