Big Ramsey degrees in the metric setting

Autor:	Bice, Tristan, de Rancourt, Noé, Hubička, Jan, Konečný, Matěj
Rok vydání:	2023
Předmět:	Mathematics - Functional Analysis Computer Science - Discrete Mathematics Mathematics - Combinatorics Mathematics - Logic 05D10 05C05 05C55 54E35 46B20 G.2.2 F.4.1
Druh dokumentu:	Working Paper
Popis:	Oscillation stability is an important concept in Banach space theory which happens to be closely connected to discrete Ramsey theory. For example, Gowers proved oscillation stability for the Banach space $c_0$ using his now famous Ramsey theorem for $\mathrm{FIN}_k$ as the key ingredient. We develop the theory behind this connection and introduce the notion of compact big Ramsey degrees, extending the theory of (discrete) big Ramsey degrees. We then prove existence of compact big Ramsey degrees for the Banach space $\ell_\infty$ and the Urysohn sphere, with an explicit characterization in the case of $\ell_\infty$. Comment: 6 pages; extended abstract
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.14577 Zobrazit plný text záznamu View this record from Arxiv