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

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Lionel Nguyen van Thé

#### 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.

#### Domains

Mathematics [math] Combinatorics [math.CO]

### Dates and versions

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

### Identifiers

• HAL Id : hal-03347359 , version 1
• ARXIV :

### Cite

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

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