Fra\"iss\'e limit and Ramsey Theorem: the case of MV-algebras and a categorical generalization

Abstract

In this paper we describe the Fra\"iss\'e 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 minumum 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.