5 citations · 20 across the 15 of their papers we have counts for
16 papers
Tree-like graphings, wallings, and median graphings of equivalence relations
Ruiyuan Chen, Antoine Poulin, Ran Tao +1
We prove several results showing that every locally finite Borel graph whose large-scale geometry is "tree-like" induces a treeable equivalence relation. In particular, our hypothe…
A Gelfand duality for continuous lattices
Ruiyuan Chen
We prove that the category of continuous lattices and meet- and directed join-preserving maps is dually equivalent, via the hom functor to , to the category of complete Arch…
Nonamenable subforests of multi-ended quasi-pmp graphs
Ruiyuan Chen, Grigory Terlov, Anush Tserunyan
We prove the a.e. nonamenability of locally finite quasi-pmp Borel graphs whose every component admits at least three nonvanishing ends with respect to the underlying Radon--Nikody…
Structural, point-free, non-Hausdorff topological realization of Borel groupoid actions
Ruiyuan Chen
We extend the Becker--Kechris topological realization and change-of-topology theorems for Polish group actions in several directions. For Polish group actions, we prove a single re…
On the Pettis-Johnstone theorem for localic groups
Ruiyuan Chen
We explain how Johnstone's 1989 proof of the closed subgroup theorem for localic groups can be viewed as a point-free version of Pettis's theorem for Baire topological groups. We t…
On sifted colimits in the presence of pullbacks
Ruiyuan Chen
We show that in a category with pullbacks, arbitrary sifted colimits may be constructed as filtered colimits of reflexive coequalizers. This implies that "lex sifted colimits", in…
Borel and analytic sets in locales
Ruiyuan Chen
We systematically develop analogs of basic concepts from classical descriptive set theory in the context of pointless topology. Our starting point is to take the elements of the fr…
Representing Polish groupoids via metric structures
Ruiyuan Chen
We prove that every open -locally Polish groupoid is Borel equivalent to the groupoid of models on the Urysohn sphere of an -sentence in con…
A universal characterization of standard Borel spaces
Ruiyuan Chen
We prove that the category of standard Borel spaces is the (bi-)initial object in the 2-category of countably complete Boolean (countably) extensive categories. Thi…
Bounds on Continuous Scott Rank
William Chan, Ruiyuan Chen
An analog of Nadel's effective bound for the continuous Scott rank of metric structures, developed by Ben Yaacov, Doucha, Nies, and Tsankov, will be established: Let …
Notes on quasi-Polish spaces
Ruiyuan Chen
Quasi-Polish spaces were introduced by de Brecht as a possibly non-Hausdorff generalization of Polish spaces sharing many of their descriptive set-theoretic properties. We give a s…
Decompositions and measures on countable Borel equivalence relations
Ruiyuan Chen
We show that the uniform measure-theoretic ergodic decomposition of a countable Borel equivalence relation may be realized as the topological ergodic decomposition of a co…
Borel functors, interpretations, and strong conceptual completeness for
Ruiyuan Chen
We prove a strong conceptual completeness theorem (in the sense of Makkai) for the infinitary logic : every countable -theory can be canonical…
Borel structurability by locally finite simplicial complexes
Ruiyuan Chen
We show that every countable Borel equivalence relation structurable by -dimensional contractible simplicial complexes embeds into one which is structurable by such complexes wi…
Amalgamable diagram shapes
Ruiyuan Chen
A category has the amalgamation property (AP) if every pushout diagram has a cocone, and the joint embedding property (JEP) if every finite coproduct diagram has a cocone. We show…
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…