Big Ramsey degrees and infinite languages

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00601760" target="_blank" >RIV/67985840:_____/24:00601760 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.19086/aic.2024.4" target="_blank" >https://doi.org/10.19086/aic.2024.4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.19086/aic.2024.4" target="_blank" >10.19086/aic.2024.4</a>

Result language
angličtina
Original language name
Big Ramsey degrees and infinite languages
Original language description
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.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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