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arXiv:1705.10582 [math.CO]AbstractReferencesReviewsResources

Finite Ramsey degrees and Fraïssé expansions with the Ramsey property

Lionel Nguyen Van Thé

Published 2017-05-30Version 1

By a result of Zucker, every Fra\"iss\'e structure $\bf F$ for which the elements of $\mathrm{Age}(\bf F)$ have finite Ramsey degrees admits a Fra\"iss\'e precompact expansion $\bf F^{*}$ whose age $\mathrm{Age}(\bf F^{*})$ has the Ramsey property. While the original method uses dynamics in spaces of ultrafilters, the purpose of the present short note is to provide a different proof, based on classical tools from Fra\"iss\'e theory.

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