35 citations · 138 across the 26 of their papers we have counts for
5 papers · 1 filter
Infinite time decidable equivalence relation theory
Samuel Coskey, Joel David Hamkins
We introduce an analog of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reducti…
Borel reductions of profinite actions of SL(n,Z)
Samuel Coskey
Greg Hjorth and Simon Thomas proved that the classification problem for torsion-free abelian groups of finite rank \emph{strictly increases} in complexity with the rank. Subsequent…
The complexity of classification problems for models of arithmetic
Samuel Coskey, Roman Kossak
We observe that the classification problem for countable models of arithmetic is Borel complete. On the other hand, the classification problems for finitely generated models of ari…
The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism
Samuel Coskey
The isomorphism and quasi-isomorphism relations on the -local torsion-free abelian groups of rank are incomparable with respect to Borel reducibility.
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…