Geodesic
On dual Ramsey theorems for relational structures
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 553-585.

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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.
DOI : 10.21136/CMJ.2020.0408-18
Classification : 05C55, 18A99
Keywords: dual Ramsey property; finite relational structure; category theory 
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     title = {On dual {Ramsey} theorems for relational structures},
     journal = {Czechoslovak Mathematical Journal},
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Mašulović, Dragan. On dual Ramsey theorems for relational structures. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 553-585. doi : 10.21136/CMJ.2020.0408-18. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0408-18/

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