All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
Original language description
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' 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.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ18-13685Y" target="_blank" >GJ18-13685Y: Model thoery and extremal combinatorics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
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
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Volume of the periodical
356
Issue of the periodical within the volume
listopad
Country of publishing house
US - UNITED STATES
Number of pages
89
Pages from-to
106791
UT code for WoS article
000491211800006
EID of the result in the Scopus database
2-s2.0-85071402742