2021/10/01 by Natasha Dobrinen, Dobrinen, Natasha · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2110.00655
openalex publication_date 2021/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.