Big Ramsey Degrees and Infinite Languages

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489754" target="_blank" >RIV/00216208:11320/24:10489754 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Yc~72.~IZw" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Yc~72.~IZw</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.19086/aic.2024.4" target="_blank" >10.19086/aic.2024.4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Big Ramsey Degrees and Infinite Languages

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Big Ramsey Degrees and Infinite Languages

Popis výsledku anglicky

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.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

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

2024

Kód důvěrnosti údajů

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

Název periodika

Advances in Combinatorics

ISSN

—

e-ISSN

2517-5599

Svazek periodika

2024

Číslo periodika v rámci svazku

August 10, 2024

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

26

Strana od-do

2024.4

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-85208649149