35 citations · 138 across the 26 of their papers we have counts for
20 papers · 1 filter
New jump operators on equivalence relations
John D. Clemens, Samuel Coskey
We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group we introduce the -jump. We study the elementary properties…
Computable reducibility of equivalence relations and an effective jump operator
John D. Clemens, Samuel Coskey, Gianni Krakoff
We introduce the computable FS-jump, an analog of the classical Friedman--Stanley jump in the context of equivalence relations on the natural numbers. We prove that the computable…
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…
On the classification of automorphisms of trees
Kyle Beserra, Samuel Coskey
We identify the complexity of the classification problem for automorphisms of a given countable regularly branching tree up to conjugacy. We consider both the rooted and unrooted c…
The classification of countable models of set theory
John Clemens, Samuel Coskey, Samuel Dworetzky
We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel compl…
On the classification of vertex-transitive structures
John Clemens, Samuel Coskey, Stephanie Potter
We consider the classification problem for several classes of countable structures which are "vertex-transitive", meaning that the automorphism group acts transitively on the eleme…
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…
Generalized Choquet spaces
Samuel Coskey, Philipp Schlicht
We introduce an analog to the notion of Polish space for spaces of weight , where is an uncountable regular cardinal such that . Specifically, we consider spac…
Ioana's superrigidity theorem and orbit equivalence relations
Samuel Coskey
In this expository article, we give a survey of Adrian Ioana's cocycle superrigidity theorem for profinite actions of Property (T) groups, and its applications to ergodic theory an…
Borel Tukey morphisms and combinatorial cardinal invariants of the continuum
Samuel Coskey, Tamás Mátrai, Juris Steprāns
We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been cons…
The hierarchy of equivalence relations on the natural numbers under computable reducibility
Samuel Coskey, Joel David Hamkins, Russell Miller
The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computab…
Cardinal characteristics and countable Borel equivalence relations
Samuel Coskey, Scott Schneider
Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for h…
Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals
Samuel Coskey, Joel David Hamkins
We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite…
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…