4 citations · 11 across the 9 of their papers we have counts for
9 papers
Tukey morphisms between finite relations
Rhett Barton, Samuel Coskey, Paul Ellis
We investigate Tukey morphisms between binary relations, establishing several fundamental lemmas. We then specialize to finite binary relations, using computational methods to clas…
The Arithmetic-Periodicity of \textsc{cut} for
Paul Ellis, Thotsaporn Aek Thanatipanonda
\textsc{cut} is a class of partition games played on a finite number of finite piles of tokens. Each version of \textsc{cut} is specified by a cut-set $\mathcal{C}\subseteq\mathbb{…
Reducing the dichromatic number via cycle reversions in infinite digraphs
Paul Ellis, Attila Joó, Dániel T. Soukup
We prove the following conjecture of S. Thomassé: for every (potentially infinite) digraph it is possible to iteratively reverse directed cycles in such a way that the dichro…
Conjugacy for homogeneous ordered graphs
Samuel Coskey, Paul Ellis
We show that for any countable homogeneous ordered graph , the conjugacy problem for automorphisms of is Borel complete. In fact we establish that each such satisfies a…
The Classification Problem for Simple Unital Finite Rank Dimension Groups
Paul Ellis
The Borel complexity of the isomorphism problem for finite-rank unital simple dimension groups increases with rank. This implies that the isomorphism problems for the corresponding…
The conjugacy problem for automorphism groups of homogeneous digraphs
Samuel Coskey, Paul Ellis
We decide the Borel complexity of the conjugacy problem for automorphism groups of countable homogeneous digraphs. Many of the homogeneous digraphs, as well as several other homoge…
The conjugacy problem for automorphism groups of countable homogeneous structures
Samuel Coskey, Paul Ellis
We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation…
A López-Escobar theorem for metric structures, and the topological Vaught conjecture
Samuel Coskey, Martino Lupini
We show that a version of López-Escobar's theorem holds in the setting of logic for metric structures. More precisely, let denote the Urysohn sphere and let $\mathrm{M…
The conjugacy problem for the automorphism group of the random graph
Samuel Coskey, Paul Ellis, Scott Schneider
We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structu…