On Dual Ramsey Theorems for Relational Structures

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.

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Correspondence to Dragan Mašulović.

Additional information

The author gratefully acknowledges the support of the Grant No. 174019 of the Ministry of Education, Science and Technological Development of the Republic of Serbia.

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Mašulović, D. On Dual Ramsey Theorems for Relational Structures. Czech Math J 70, 553–585 (2020). https://doi.org/10.21136/CMJ.2020.0408-18

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Keywords

  • dual Ramsey property
  • finite relational structure
  • category theory

MSC 2010

  • 05C55
  • 18A99