Czechoslovak Mathematical Journal, Vol. 70, No. 2, pp. 553-585, 2020
On dual Ramsey theorems for relational structures
Received September 18, 2018. Published online February 7, 2020.
Abstract: We discuss dual Ramsey statements for several classes of finite relational structures (such as finite linearly ordered graphs, finite linearly ordered metric spaces and finite posets with a linear extension) and conclude the paper with another rendering of the Nešetřil-Rödl Theorem for relational structures. Instead of embeddings which are crucial for "direct" Ramsey results, for each class of structures under consideration we propose a special class of quotient maps and prove a dual Ramsey theorem in such a setting. Although our methods are based on reinterpreting the (dual) Ramsey property in the language of category theory, all our results are about classes of finite structures.
Keywords: dual Ramsey property; finite relational structure; category theory
Affiliations: Dragan Mašulović, Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića, 21000 Novi Sad, Serbia, e-mail: email@example.com