Is Ramsey's Theorem omega-automatic?

Kuske, Dietrich

doi:10.4230/LIPIcs.STACS.2010.2483

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Is Ramsey's Theorem omega-automatic?

Author Dietrich Kuske

Part of: Volume: 27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution-NoDerivs 3.0 Unported license
Publication Date: 2010-03-09

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DOI: 10.4230/LIPIcs.STACS.2010.2483
URN: urn:nbn:de:0030-drops-24838

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Keywords

Logic in computer science
automata
Ramsey theory

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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 As Get BibTex

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

Author Details

Dietrich Kuske

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