Big Ramsey degrees and forbidden cycles
Martin Balko, David Chodounsk\'y, Jan Hubi\v{c}ka, Mat\v{e}j, Kone\v{c}n\'y, Jaroslav Ne\v{s}et\v{r}il, and Llu\'is Vena
TL;DR
This paper introduces a new general condition, based on the Carlson-Simpson theorem, that determines when structures in finite binary relational languages have finite big Ramsey degrees.
Contribution
It provides a novel criterion for finite big Ramsey degrees in structures within finite binary relational languages, expanding understanding in Ramsey theory.
Findings
Established a new condition for finite big Ramsey degrees.
Applied the Carlson-Simpson theorem to relational structures.
Enhanced the theoretical framework for Ramsey degrees in finite languages.
Abstract
Using the Carlson-Simpson theorem, we give a new general condition for a structure in a finite binary relational language to have finite big Ramsey degrees
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · semigroups and automata theory