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Finite Ramsey degrees and Fra\"iss\'e expansions with the Ramsey property

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Abstract

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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hal-03347359 , version 1 (17-09-2021)

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Lionel Nguyen van Thé. Finite Ramsey degrees and Fra\"iss\'e expansions with the Ramsey property. 2021. ⟨hal-03347359⟩
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