A dichotomy for countable unions of smooth Borel equivalence relations

De Rancourt, Noé; Miller, Benjamin

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

A dichotomy for countable unions of smooth Borel equivalence relations

Author(s) :

De Rancourt, Noé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Universität Wien = University of Vienna
Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic] [UK]
Miller, Benjamin [Auteur]
Universität Wien = University of Vienna

Journal title :

The Journal of Symbolic Logic

Publisher :

Association for Symbolic Logic

Publication date :

2024

ISSN :

0022-4812

English keyword(s) :

Countable equivalence relation
Dichotomy
Intersection graph
Smooth equivalence relation

HAL domain(s) :

Mathématiques [math]/Logique [math.LO]

English abstract : [en]

We show that if an equivalence relation $E$ on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of $E$ to a countable Borel equivalence relation on a ...
Show more >We show that if an equivalence relation $E$ on a Polish space is a countable union of smooth Borel subequivalence relations, then there is either a Borel reduction of $E$ to a countable Borel equivalence relation on a Polish space or a continuous embedding of $\mathbb{E}_1$ into $E$. We also establish related results concerning countable unions of more general Borel equivalence relations.Show less >

Language :

Anglais

Popular science :

Non

Collections :