Ruiyuan Chen

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math.LO2025

Optimal Syntactic Definitions of Back-and-Forth Types

Ruiyuan Chen, David Gonzalez, Matthew Harrison-Trainor

The back-and-forth relations $M \leq_{I^} \pm N$ are central to computable structure theory and countable model theory. It is well-known that the relation ${(M, N) : M \leq_{I^} \pm N}$ is (ligh…

math.LO2025

Componentwise Polish groupoids and equivalence relations

Ruiyuan Chen

We study Borel equivalence relations equipped with a uniformly Borel family of Polish topologies on each equivalence class, and more generally, standard Borel groupoids equipped wi…

math.LO2024

Structurable equivalence relations and $L_{I ¨ _{1} I ¨ }$ interpretations

Rishi Banerjee, Ruiyuan Chen

We show that the category of countable Borel equivalence relations (CBERs) is dually equivalent to the category of countable $L_{I ¨ _{1} I ¨ }$ theories which admit a one-sorte…

math.LO2024

Clones of Borel Boolean Functions

Ruiyuan Chen, Ilir Ziba

We study the lattice of all Borel clones on $2 = {0, 1}$ : classes of Borel functions $f : 2^{n} \to 2$ , $n \leq I ¨ $ , which are closed under composition and include all projections. T…

Optimal Syntactic Definitions of Back-and-Forth Types

Componentwise Polish groupoids and equivalence relations

Structurable equivalence relations and LI¨1​I¨​ interpretations

Clones of Borel Boolean Functions

Structurable equivalence relations and $L_{I ¨ _{1} I ¨ }$ interpretations