54 citations · 178 across the 18 of their papers we have counts for
6 papers · 2 filters
Borel Circle Squaring
Andrew S. Marks, Spencer T. Unger
We give a completely constructive solution to Tarski's circle squaring problem. More generally, we prove a Borel version of an equidecomposition theorem due to Laczkovich. If $k \g…
Hyperfiniteness and Borel combinatorics
Clinton Conley, Steve Jackson, Andrew Marks +2
We study the relationship between hyperfiniteness and problems in Borel graph combinatorics by adapting game-theoretic techniques introduced by Marks to the hyperfinite setting. We…
Uniformity, Universality, and Computability Theory
Andrew S Marks
We prove a number of results motivated by global questions of uniformity in computability theory, and universality of countable Borel equivalence relations. Our main technical tool…
Jump operations for Borel graphs
Adam R. Day, Andrew S. Marks
We investigate the class of bipartite Borel graphs organized by the order of Borel homomorphism. We show that this class is unbounded by finding a jump operator for Borel graphs an…
Brooks's theorem for measurable colorings
Clinton T. Conley, Andrew S. Marks, Robin Tucker-Drob
We generalize Brooks's theorem to show that if is a Borel graph on a standard Borel space of degree bounded by which contains no -cliques, then admits…
The universality of polynomial time Turing equivalence
Andrew S. Marks
We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence rela…