Assaf Shani

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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 = I ¨ $ . We prove a dichotomy for Borel homomorphisms from the $n$ -th Friedman-Stanley jump $=^{+ n}$ to an equivalence relation $E$ which is classifiable by c…

math.LO2024

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 I ¨ $ , so that for all $A \subseteq N$ of size $n + 1$ , the orbit of…

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 phenomena for Bernoulli shifts of bounded algebraic dimension

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