Assaf Shani

activity

20182025

most citedBorel reducibility and symmetric models

7 citations · 10 across the 11 of their papers we have counts for

collaborators

11 papers

math.LO2025

A counterexample regarding an equivalence relation on a product space

Assaf Shani

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.

math.LO2024

Generic dichotomy for homomorphisms for $E_{0}^{N}$

Assaf Shani

We prove the following dichotomy. Given an analytic equivalence relation $E$ , either $E_{0}^{N} \leq_{B} E$ or else any Borel homomorphism from $E_{0}^{N}$ to $E$ is…

math.LO2024

Intermediate models with deep failure of choice

Yair Hayut, Assaf Shani

The following question was asked by Grigorieff: Suppose $V$ is a ZFC model and $V [G]$ is a set-generic extension of $V$ . Can there be a ZF model $N$ so that $V\subset N \subset V[G…

math.LO2024

The finite Friedman-Stanley jumps: generic dichotomies for Borel homomorphisms

Assaf Shani

Fix $n = 1, 2, 3, \dots$ or $n = ω$ . We prove a dichotomy for Borel homomorphisms from the $n$ -th Friedman-Stanley jump $=^{+ n}$ to an equivalence relation $E$ which is classifiable by co…

math.LO2022

Strong ergodicity for the Gamma-jump operator and for actions of Polish wreath products

Assaf Shani

Let $Γ$ and $Δ$ be sufficiently distinct countable groups. We show that there is an orbit equivalence relation $E$ , induced by an action of the Polish wreath product group $Γ ≀ Γ$ ,…

math.LO2021

Classifying invariants for $E_{1}$ : A tail of a generic real

Assaf Shani

Let $E$ be an analytic equivalence relation on a Polish space. We introduce a framework for studying the possible "reasonable" complete classifications and the complexity of possib…

math.LO2021

Actions of tame abelian product groups

Shaun Allison, Assaf Shani

A Polish group $G$ is tame if for any continuous action of $G$ , the corresponding orbit equivalence relation is Borel. When $G = \prod_{n} Γ_{n}$ for countable abelian $Γ_{n}$ , Solecki (…

math.LO2021

Strong ergodicity phenomena for Bernoulli shifts of bounded algebraic dimension

Aristotelis Panagiotopoulos, Assaf Shani

The algebraic dimension of a Polish permutation group $Q \leq Sym (N)$ is the smallest $n \in ω$ , so that for all $A \subseteq N$ of size $n + 1$ , the orbit of…

math.LO2020

Anti-classification results for groups acting freely on the line

Filippo Calderoni, David Marker, Luca Motto Ros +1

We explore countable ordered Archimedean groups from the point of view of descriptive set theory. We introduce the space of Archimedean left-orderings $Ar (G)$ for a given…

math.LO2019★ 3 cited

Strong ergodicity around countable products of countable equivalence relations

Assaf Shani

This paper deals with countable products of countable Borel equivalence relations and equivalence relations "just above" those in the Borel reducibility hierarchy. We show that if…

math.LO2018★ 7 cited

Borel reducibility and symmetric models

Assaf Shani

We develop a correspondence between the study of Borel equivalence relations induced by closed subgroups of $S_{\infty}$ , and the study of symmetric models and weak choice principles…

A counterexample regarding an equivalence relation on a product space

Generic dichotomy for homomorphisms for E0N​

Intermediate models with deep failure of choice

The finite Friedman-Stanley jumps: generic dichotomies for Borel homomorphisms

Strong ergodicity for the Gamma-jump operator and for actions of Polish wreath products

Classifying invariants for E1​: A tail of a generic real

Actions of tame abelian product groups

Strong ergodicity phenomena for Bernoulli shifts of bounded algebraic dimension

Anti-classification results for groups acting freely on the line

Strong ergodicity around countable products of countable equivalence relations

Borel reducibility and symmetric models

Generic dichotomy for homomorphisms for $E_{0}^{N}$

Classifying invariants for $E_{1}$ : A tail of a generic real