All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401525" target="_blank" >RIV/00216208:11320/19:10401525 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=igQGUo7d0P" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=igQGUo7d0P</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aim.2019.106791" target="_blank" >10.1016/j.aim.2019.106791</a>

Jazyk výsledku

angličtina

Název v původním jazyce

All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)

Popis výsledku v původním jazyce

We prove the Ramsey property for classes of ordered structures with closures and given local properties. This generalises earlier results: the Negetfil-Rodl Theorem, the Ramsey property of partial orders and metric spaces as well as the authors&apos; Ramsey lift of bowtie-free graphs. We use this framework to solve several open problems and give new examples of Ramsey classes. Among others, we find Ramsey lifts of convexly ordered S-metric spaces and prove the Ramsey theorem for finite models (i.e. structures with both functions and relations) thus providing the ultimate generalisation of the structural Ramsey theorem. Both of these results are natural, and easy to state, yet their proofs involve most of the theory developed here. We also characterise Ramsey lifts of classes of structures defined by finitely many forbidden homomorphisms and extend this to special cases of classes with closures. This has numerous applications. For example, we find Ramsey lifts of many C herlin-Shelah-S hi classes. (C) 2019 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)

Popis výsledku anglicky

We prove the Ramsey property for classes of ordered structures with closures and given local properties. This generalises earlier results: the Negetfil-Rodl Theorem, the Ramsey property of partial orders and metric spaces as well as the authors&apos; Ramsey lift of bowtie-free graphs. We use this framework to solve several open problems and give new examples of Ramsey classes. Among others, we find Ramsey lifts of convexly ordered S-metric spaces and prove the Ramsey theorem for finite models (i.e. structures with both functions and relations) thus providing the ultimate generalisation of the structural Ramsey theorem. Both of these results are natural, and easy to state, yet their proofs involve most of the theory developed here. We also characterise Ramsey lifts of classes of structures defined by finitely many forbidden homomorphisms and extend this to special cases of classes with closures. This has numerous applications. For example, we find Ramsey lifts of many C herlin-Shelah-S hi classes. (C) 2019 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ18-13685Y" target="_blank" >GJ18-13685Y: Teorie modelů a extrémální kombinatorika</a><br>

Návaznosti

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

Rok uplatnění

2019

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

—

Svazek periodika

356

Číslo periodika v rámci svazku

listopad

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

89

Strana od-do

106791

Kód UT WoS článku

000491211800006

EID výsledku v databázi Scopus

2-s2.0-85071402742