Geodesic
Big Ramsey Degrees and Infinite Languages
Advances in Combinatronics (2024)

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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.
Publié le : 
@article{ADVC_2024_a3,
     author = {Samuel Braunfeld and David Chodounsk\'y and No\'e de Rancourt and Jan Hubi\v{c}ka and Jamal Kawach and Mat\v{e}j Kone\v{c}n\'y},
     title = {Big {Ramsey} {Degrees} and {Infinite} {Languages}},
     journal = {Advances in Combinatronics},
     publisher = {mathdoc},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2024_a3/}
}
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Samuel Braunfeld; David Chodounský; Noé de Rancourt; Jan Hubička; Jamal Kawach; Matěj Konečný. Big Ramsey Degrees and Infinite Languages. Advances in Combinatronics (2024). http://geodesic.mathdoc.fr/item/ADVC_2024_a3/