54 citations · 178 across the 18 of their papers we have counts for
20 papers
Borel dimension growth and hyperfiniteness
Jan Grebík, Andrew S. Marks, Václav Rozhoň +1
We show that every increasing union of Borel graphs of pointwise volume growth at most is hyperfinite, where is the unique real root of $(1 - γ)^3…
Hausdorff dimension and countable Borel equivalence relations
Andrew Marks, Dino Rossegger, Theodore Slaman
We show that if is a countable Borel equivalence relation on , then there is a closed subset of Hausdorff dimension so that $E \restrictio…
One-ended spanning subforests and treeability of groups
Clinton T. Conley, Damien Gaboriau, Andrew S. Marks +1
We show that several new classes of groups are measure strongly treeable. In particular, finitely generated groups admitting planar Cayley graphs, elementarily free groups, and the…
Borel asymptotic dimension and hyperfinite equivalence relations
Clinton Conley, Steve Jackson, Andrew Marks +2
A long standing open problem in the theory of hyperfinite equivalence relations asks if the orbit equivalence relation generated by a Borel action of a countable amenable group is…
On a question of Slaman and Steel
Adam Day, Andrew Marks
We consider an old question of Slaman and Steel: whether Turing equivalence is an increasing union of Borel equivalence relations none of which contain a uniformly computable infin…
Measurable realizations of abstract systems of congruences
Clinton T. Conley, Andrew S. Marks, Spencer T. Unger
An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congrue…