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

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.
Document type :
Preprints, Working Papers, ...

https://hal-amu.archives-ouvertes.fr/hal-03347359
Contributor : Lionel Nguyen Van Thé Connect in order to contact the contributor
Submitted on : Friday, September 17, 2021 - 10:44:44 AM
Last modification on : Wednesday, February 9, 2022 - 11:02:03 AM

### Identifiers

• HAL Id : hal-03347359, version 1
• ARXIV : 1705.10582

### Citation

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

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