Big Ramsey degrees using parameter spaces
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Big Ramsey degrees using parameter spaces
Original language description
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 & 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 & 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA21-10775S" target="_blank" >GA21-10775S: Ramsey theory in the context of group theory, model theory and topological dynamics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Mathematics
ISSN
0001-8708
e-ISSN
1090-2082
Volume of the periodical
478
Issue of the periodical within the volume
Neuveden
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
110386
UT code for WoS article
001509050300003
EID of the result in the Scopus database
2-s2.0-105007498804