Big Ramsey degrees using parameter spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10499791" target="_blank" >RIV/00216208:11320/25:10499791 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DK65hST5-H" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=DK65hST5-H</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2025.110386" target="_blank" >10.1016/j.aim.2025.110386</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Big Ramsey degrees using parameter spaces

Popis výsledku v původním jazyce

We show that the universal homogeneous partial order has finite big Ramsey degrees and discuss several corollaries. Our proof relies on parameter spaces and the Carlson-Simpson theorem rather than on (a strengthening of) the Halpern-L &amp; auml;uchli theorem and the Milliken tree theorem, which are typically used to bound big Ramsey degrees in the existing literature (originating from the work of Laver and Milliken). This new technique has many additional applications. We show that the homogeneous universal triangle-free graph has finite big Ramsey degrees, providing a short proof of a recent result by Dobrinen. Moreover, generalizing an indivisibility (vertex partition) result of Nguyen van Th &amp; eacute; and Sauer, we give an upper bound on big Ramsey degrees of metric spaces with finitely many distances. This leads to a new combinatorial argument for the oscillation stability of the Urysohn Sphere. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Název v anglickém jazyce

Big Ramsey degrees using parameter spaces

Popis výsledku anglicky

We show that the universal homogeneous partial order has finite big Ramsey degrees and discuss several corollaries. Our proof relies on parameter spaces and the Carlson-Simpson theorem rather than on (a strengthening of) the Halpern-L &amp; auml;uchli theorem and the Milliken tree theorem, which are typically used to bound big Ramsey degrees in the existing literature (originating from the work of Laver and Milliken). This new technique has many additional applications. We show that the homogeneous universal triangle-free graph has finite big Ramsey degrees, providing a short proof of a recent result by Dobrinen. Moreover, generalizing an indivisibility (vertex partition) result of Nguyen van Th &amp; eacute; and Sauer, we give an upper bound on big Ramsey degrees of metric spaces with finitely many distances. This leads to a new combinatorial argument for the oscillation stability of the Urysohn Sphere. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA21-10775S" target="_blank" >GA21-10775S: Ramseyova teorie v kontextu teorie grup, teorie modelů a topologické dynamiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Advances in Mathematics

ISSN

0001-8708

e-ISSN

1090-2082

Svazek periodika

478

Číslo periodika v rámci svazku

Neuveden

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

110386

Kód UT WoS článku

001509050300003

EID výsledku v databázi Scopus

2-s2.0-105007498804