4 citations · 12 across the 9 of their papers we have counts for
9 papers
The set of distances in a Polish metric space
John D. Clemens
We show that a set of non-negative reals is the distance set of a separable complete metric space if and only if it is either countable or is an analytic set which has 0 as a limit…
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…
Relative primeness and Borel partition properties for equivalence relations
John D. Clemens
We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that…
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…
Doubly Robust Estimation in Observational Studies with Partial Interference
Lan Liu, Michael G. Hudgens, Bradley Saul +3
Interference occurs when the treatment (or exposure) of one individual affects the outcomes of others. In some settings it may be reasonable to assume individuals can be partitione…
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…
Dichotomy Theorems for Families of Non-Cofinal Essential Complexity
John D. Clemens, Dominique Lecomte, Benjamin D. Miller
We prove that for every Borel equivalence relation , either is Borel reducible to , or the family of Borel equivalence relations incompatible with has cof…
Essential countability of treeable equivalence relations
Dominique Lecomte, John D. Clemens, Benjamin D. Miller
We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumpt…