16 citations · 24 across the 12 of their papers we have counts for
13 papers
Randomized Borel -coloring of digraphs
Anton Bernshteyn, Edward Hou, Forte Shinko +1
Let be a Borel digraph with maximum out-degree . We show that admits a random Borel -coloring for which every edge is almost surely not monochroma…
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…
Hyperfiniteness of bounded-to-one actions of commutative monoids
Forte Shinko, Felix Weilacher, Jing Yu
A theorem of Dougherty--Jackson--Kechris states that any equivalence relation generated by a single Borel function is hypersmooth. A well-known open problem is whether this can be…
Hyper-hyperfiniteness and complexity
Joshua Frisch, Forte Shinko, Zoltan Vidnyanszky
We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite, then the complexity of hyperfinite countable Borel equivalence r…
Asymptotic dimension and hyperfiniteness of generic Cantor actions
Sumun Iyer, Forte Shinko
We show that for a countable discrete group which is locally of finite asymptotic dimension, the generic continuous action on Cantor space has hyperfinite orbit equivalence relatio…
Hyperfiniteness for group actions on trees
Srivatsav Kunnawalkam Elayavalli, Koichi Oyakawa, Forte Shinko +1
We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Bore…
Realizations of countable Borel equivalence relations
Joshua Frisch, Alexander Kechris, Forte Shinko +1
We study topological realizations of countable Borel equivalence relations, including realizations by continuous actions of countable groups, with additional desirable properties.…
Lifts of Borel actions on quotient spaces
Joshua Frisch, Alexander Kechris, Forte Shinko
Given a countable Borel equivalence relation E and a countable group G, we study the problem of when a Borel action of G on X/E can be lifted to a Borel action of G on X.
A dichotomy for Polish modules
Joshua Frisch, Forte Shinko
Let be a ring equipped with a proper norm. We show that under suitable conditions on , there is a natural basis under continuous linear injection for the set of Polish -m…
Equidecomposition in cardinal algebras
Forte Shinko
Let be a countable group. A classical theorem of Thorisson states that if is a standard Borel -space and and are Borel probability measures on which agree on…
Quotients by countable subgroups are hyperfinite
Joshua Frisch, Forte Shinko
We show that for any Polish group and any countable normal subgroup , the coset equivalence relation is a hyperfinite Borel equivalence relation. In par…
Hyperfiniteness of boundary actions of cubulated hyperbolic groups
Jingyin Huang, Marcin Sabok, Forte Shinko
We show that if a hyperbolic group acts geometrically on a CAT(0) cube complex, then the induced boundary action is hyperfinite. This means that for a cubulated hyperbolic group th…
Differential polynomial rings over rings satisfying a polynomial identity
Jason P. Bell, Blake W. Madill, Forte Shinko
Let be a ring satisfying a polynomial identity and let be a derivation of . We show that if is the nil radical of then and the Jacobson radical…