9 citations · 25 across the 13 of their papers we have counts for
13 papers · 1 filter
Borel graphable equivalence relations
Tyler Arant, Alexander S. Kechris, Patrick Lutz
This paper is devoted to the study of analytic equivalence relations which are Borel graphable, i.e. which can be realized as the connectedness relation of a Borel graph. Our main…
Invariant uniformization
Alexander S. Kechris, Michael Wolman
Standard results in descriptive set theory provide sufficient conditions for a Borel set to admit a Borel uniformiz…
An effective version of Nadkarni's Theorem
Alexander S. Kechris, Michael S. Wolman
Nadkarni's Theorem asserts that for a countable Borel equivalence relation (CBER) exactly one of the following holds: (1) It has an invariant Borel probability measure or (2) it ad…
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.
On Polish groups admitting non-essentially countable actions
Alexander S. Kechris, Maciej Malicki, Aristotelis Panagiotopoulos +1
It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relati…
Co-induction and Invariant Random Subgroups
Alexander S. Kechris, Vibeke Quorning
In this paper we develop a co-induction operation which transforms an invariant random subgroup of a group into an invariant random subgroup of a larger group. We use this operatio…
The complexity of topological group isomorphism
Alexander S. Kechris, Andree Nies, Katrin Tent
We study the complexity of the isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducib…
Structurable equivalence relations
Ruiyuan Chen, Alexander S. Kechris
For a class of countable relational structures, a countable Borel equivalence relation is said to be -structurable if there is a Borel way to put a str…
Turbulence, amalgamation and generic automorphisms of homogeneous structures
Alexander S. Kechris, Christian Rosendal
We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of…
Fraisse Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups
A. S. Kechris, V. G. Pestov, S. Todorcevic
We study in this paper some connections between the Fraisse theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism…
How many Turing degrees are there?
Randall Dougherty, Alexander S. Kechris
A Borel equivalence relation on a Polish space is said to be countable if all of its equivalence classes are countable. Standard examples of countable Borel equivalence relations (…
Borel actions of Polish groups
Howard Becker, Alexander S. Kechris
We show that a {\it Borel} action of a Polish group on a standard Borel space is Borel isomorphic to a {\it continuous} action of the group on a Polish space, and we apply this res…