相关论文: Some new results on Borel irreducibility of equiva…

We develop general machinery to cast the class of potential canonical Scott sentences of an infinitary sentence $\Phi$ as a class of structures in a related language. From this, we show that $\Phi$ has a Borel complete expansion if and only…

We consider when finite families $F \subseteq \mathbb{C}[t]$ of bounded degree polynomials, or more generally of bounded complexity finite-to-finite correspondences on $\mathbb{C}$, can exhibit non-expansion of the form $|F(A)| =…

Let $\mathcal{R}$ be a free Lie conformal algebra of rank $2$ with $\mathbb{C}[\partial]$-basis $\{L,I\}$ and relations \begin{eqnarray*} \left[L_{\lambda} L\right]=(\partial+2 \lambda) (L+I),\ \left[L_{\lambda} I\right]=(\partial+\lambda)…

In the late $70$'s Feldman and Moore defined the cohomology associated to a countable equivalence relation with coefficients in an Abelian Polish group. When the equivalence relation is the orbital one, that is it is induced by a measure…

We introduce and investigate different definitions of effective amenability, in terms of computability of F{\o}lner sets, Reiter functions, and F{\o}lner functions. As a consequence, we prove that recursively presented amenable groups have…

We prove that non-Hilbertian separable Orlicz sequence spaces are ergodic, i.e., the equivalence relation $\mathbb{E}_0$ Borel reduces to the isomorphism relation between subspaces of every such space. This is done by exhibiting…

The goals of this paper are twofold. First, we generalize the result of Gaboriau and Lyons [GL07] to the setting of von Neumann's problem for equivalence relations, proving that for any non-amenable ergodic probability measure preserving…

The concept of a C-approximable group, for a class of finite groups C, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised the question whether all groups are approximable by finite…

We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism),…

We show that every basis for the countable Borel equivalence relations strictly above $\mathbb{E}_0$ under measure reducibility is uncountable, thereby ruling out natural generalizations of the Glimm-Effros dichotomy. We also push many…

We show that for any Polish group $G$ and any countable normal subgroup $\Gamma\triangleleft G$, the coset equivalence relation $G/\Gamma$ is a hyperfinite Borel equivalence relation. In particular, the outer automorphism group of any…

We give, for some Borel sets of a product of two Polish spaces, including the Borel sets with countable sections, a Hurewicz-like characterization of those which cannot become a transfinite difference of open sets by changing the two Polish…

Let $G$ be a reductive group over a non-archimedean local field $F$ of residue characteristic $p$. We prove that the Hecke algebras of $G(F)$ with coefficients in a ${\mathbb Z}_{\ell}$-algebra $R$ for $\ell$ not equal to $p$ are finitely…

Under a mild definability assumption, we characterize the family of Borel actions $\Gamma \curvearrowright X$ of tsi Polish groups on Polish spaces that can be decomposed into countably-many actions admitting complete Borel sets that are…

Given a countable group G, we consider the sets S_factor(G), S_eqrel(G), of subgroups F of the positive real line for which there exists a free ergodic probability measure preserving action G on X such that the fundamental group of the…

Hjorth has introduced a Scott analysis for general Polish group actions, and has asked whether his notion of rank satisfies a boundedness principle similar to the one of Scott rank - namely, the orbit equivalence relation is Borel if and…

For any $2\leq n\leq \infty$, we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $\Bbb F_n$. These actions arise as diagonal products between a generalized Bernoulli action and the action $\Bbb…

We give a new short proof of the theorem due to Marquis and Sabok, which states that the orbit equivalence relation induced by the action of a finitely generated hyperbolic group on its Gromov boundary is hyperfinite. Our methods permit…

If $(X,d)$ is a Polish metric space of dimension $0$, then by Wadge's lemma, no more than two Borel subsets of $X$ can be incomparable with respect to continuous reducibility. In contrast, our main result shows that for any metric space…

We show that the category of countable Borel equivalence relations (CBERs) is dually equivalent to the category of countable $\mathcal{L}_{\omega_1\omega}$ theories which admit a one-sorted interpretation of a particular theory we call…