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arXiv · 1705.10582

Finite Ramsey degrees and Fraïssé expansions with the Ramsey property

Lionel Nguyen Van Thé
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Abstract

By a result of Zucker, every Fraïssé structure $\bf F$ for which the elements of $\mathrm{Age}(\bf F)$ have finite Ramsey degrees admits a Fraïssé 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 Fraïssé theory.

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Lionel Nguyen Van Thé. 2019-03-27. Finite Ramsey degrees and Fraïssé expansions with the Ramsey property. https://arxiv.org/abs/1705.10582

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