On dual Ramsey theorems for relational structures

Dragan Mašulović

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 2, page 553-585
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Mašulović, Dragan. "On dual Ramsey theorems for relational structures." Czechoslovak Mathematical Journal 70.2 (2020): 553-585. <http://eudml.org/doc/297381>.

@article{Mašulović2020,
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.},
author = {Mašulović, Dragan},
journal = {Czechoslovak Mathematical Journal},
keywords = {dual Ramsey property; finite relational structure; category theory},
language = {eng},
number = {2},
pages = {553-585},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On dual Ramsey theorems for relational structures},
url = {http://eudml.org/doc/297381},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Mašulović, Dragan
TI - On dual Ramsey theorems for relational structures
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 2
SP - 553
EP - 585
AB - 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.
LA - eng
KW - dual Ramsey property; finite relational structure; category theory
UR - http://eudml.org/doc/297381
ER -

References

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