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<p>In this paper we describe the Fraïssé limit of finite MV-algebras and then prove that finite MV-algebras verify the Ramsey property. Then we show that MV-algebras are just a special case of a more general situation. In fact, under minimum conditions for the application of the Kechris–Pestov–Todorcevic correspondence, Ramsey property holds for a certain category of finite structures if and only if it holds for a completion subcategory of it.</p>

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Fraïssé Limit and Ramsey Theorem: The Case of MV-Algebras and a Categorical Generalization

  • 期刊论文

  • 发表日期：

    2025年5月5日

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  • Ciro Russo

摘要

In this paper we describe the Fraïssé limit of finite MV-algebras and then prove that finite MV-algebras verify the Ramsey property. Then we show that MV-algebras are just a special case of a more general situation. In fact, under minimum conditions for the application of the Kechris–Pestov–Todorcevic correspondence, Ramsey property holds for a certain category of finite structures if and only if it holds for a completion subcategory of it.