2023/07/26 by Nadav Meir, Meir, Nadav, Aris Papadopoulos +1
Computer Science · Mathematics · #03C52 #05C55 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2307.14468
openalex publication_date 2023/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider finitary approximations of the (embedding) Ramsey property. Using a class of homogeneous reducts of random ordered hypergraphs, we prove that these properties form a strict hierarchy. We also show that every class of finite structures in which every structure of size at most 2 is a "Ramsey object" essentially consists of ordered structures, generalising a known result for countable Ramsey classes.