Big Ramsey Degrees and Infinite Languages

Autor:	Braunfeld, Samuel, Chodounský, David, de Rancourt, Noé, Hubička, Jan, Kawach, Jamal, Konečný, Matěj
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics Computer Science - Discrete Mathematics Mathematics - Logic 05D10 05C05 05C65 05C55 03C50 03C55 03E05 03E15
Zdroj:	Advances in Combinatorics 2024:4, 26pp
Druh dokumentu:	Working Paper
DOI:	10.19086/aic.2024.4
Popis:	This paper investigates big Ramsey degrees of unrestricted relational structures in (possibly) infinite languages. Despite significant progress in the study of big Ramsey degrees, the big Ramsey degrees of many classes of structures with finite small Ramsey degrees are still not well understood. We show that if there are only finitely many relations of every arity greater than one, then unrestricted relational structures have finite big Ramsey degrees, and give some evidence that this is tight. This is the first time finiteness of big Ramsey degrees has been established for a random structure in an infinite language. Our results represent an important step towards a better understanding of big Ramsey degrees for structures with relations of arity greater than two. Comment: 26 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.13116 Zobrazit plný text záznamu View this record from Arxiv