35 citations · 138 across the 26 of their papers we have counts for
27 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…
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…
On splitting and splittable families
Samuel Coskey, Bryce Frederickson, Samuel Mathers +1
A set is said to split a finite set if exactly half the elements of (up to rounding) are contained in . We study the dual notions: (1) splitting family, which is a c…
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 set splittability problem
Peter Bernstein, Cashous Bortner, Samuel Coskey +2
The set splittability problem is the following: given a finite collection of finite sets, does there exits a single set that contains exactly half the elements from each set in the…
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…
On generalizations of separating and splitting families
Daniel Condon, Samuel Coskey, Luke Serafin +1
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These famili…
The classification problem for finitely generated operator systems and spaces
Martín Argerami, Samuel Coskey, Mehrdad Kalantar +3
The classification of separable operator spaces and systems is commonly believed to be intractable. We analyze this belief from the point of view of Borel complexity theory. On one…
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…
The Fundamental Theorem on Symmetric Polynomials: History's First Whiff of Galois Theory
Ben Blum-Smith, Samuel Coskey
We describe the Fundamental Theorem on Symmetric Polynomials (FTSP), exposit a classical proof, and offer a novel proof that arose out of an informal course on group theory. The pa…
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…
Automorphisms of corona algebras, and group cohomology
Samuel Coskey, Ilijas Farah
In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded…
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…