On big Ramsey degrees for binary free amalgamation classes

2020/04/27 by Andy Zucker, Zucker, Andy · 2 citations
Computer Science · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2004.13162

openalex publication_date 2020/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalizing and simplifying recent work of Dobrinen, we show that if L is a finite binary relational language and F is a finite set of finite irreducible L-structures, then the class K = Forb(F) has finite big Ramsey degrees.

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• Counting big Ramsey degrees of the homogeneous and universal K₄-free graph
• Oscillating subalgebras of the atomless countable Boolean algebra

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