8 citations · 8 across the 6 of their papers we have counts for
6 papers
Tukey reducibility for categories -- In search of the strongest statement in finite Ramsey theory
Keegan Dasilva Barbosa, Dragan Mašulović
Every statement of the Ramsey theory of finite structures corresponds to the fact that a particular category has the Ramsey property. We can, then, compare the strength of Ramsey s…
Box Ramsey and Canonical Colourings
Keegan Dasilva Barbosa
This paper introduces the concept of a productive notion of big Ramsey degree and showcases its versatility through a handful of applications. The main focus is notably providing s…
A short note on the characterization of countable chains with finite big Ramsey spectra
Keegan Dasilva Barbosa, Dragan Mašulović, Rajko Nenadov
In this short note we confirm the deep structural correspondence between the complexity of a countable scattered chain (= strict linear order) and its big Ramsey combinatorics: we…
Borel Colouring Bad Sequences
Keegan Dasilva Barbosa
Every better quasi-order codifies a Borel graph that does not contain a copy of the shift graph. It is known that there is a better quasi-order that codes a Borel graph with infini…
A Decomposition Theorem for Aronszajn Lines
Keegan Dasilva Barbosa
We show that under the proper forcing axiom the class of all Aronszajn lines behave like -scattered orders under the embeddability relation. In particular, we are able to show t…
A Categorical Notion of Precompact Expansion
Keegan Dasilva Barbosa
We generalize the notion of relational precompact expansions of Fraïssé classes via functorial means, inspired by the technique outlined by Laflamme, Nguyen Van Thé and Sauer in th…