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Is Ramsey's Theorem omega-automatic?

Author Dietrich Kuske



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LIPIcs.STACS.2010.2483.pdf
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Dietrich Kuske

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Dietrich Kuske. Is Ramsey's Theorem omega-automatic?. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 537-548, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.STACS.2010.2483

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.
Keywords
  • Logic in computer science
  • automata
  • Ramsey theory

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