3 papers
math.LO2025
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…
math.LO2014
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…
math.LO2014
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…