Ramsey theory of homogeneous structures: current trends and open problems
Logic
2021-10-05 v1 Combinatorics
Abstract
This article highlights historical achievements in the partition theory of countable homogeneous relational structures, and presents recent work, current trends, and open problems. Exciting recent developments include new methods involving logic, topological Ramsey spaces, and category theory. The paper concentrates on big Ramsey degrees, presenting their essential structure where known and outlining areas for further development. Cognate areas, including infinite dimensional Ramsey theory of homogeneous structures and partition theory of uncountable structures, are also discussed.
Keywords
Cite
@article{arxiv.2110.00655,
title = {Ramsey theory of homogeneous structures: current trends and open problems},
author = {Natasha Dobrinen},
journal= {arXiv preprint arXiv:2110.00655},
year = {2021}
}
Comments
22 pp. To appear in the 2022 ICM Proceedings