Complexity of the isomorphism relation for Borel classes of non Archimedean groups

Speaker(s)

Andre Nies

Affiliation

University of Auckland

Language of the talk

English

Date

Aug. 13, 2025, 10 a.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

---

In the paper "The complexity of topological group isomorphism", JSL 2018, A. Kechris, the speaker and K. Tent, started the programme to determine the Borel complexity of the isomorphism relation for natural Borel classes of closed subgroups of the group Sym(N) of permutations of the natural numbers. The talk will report on progress in this research direction. 
For oligomorphic groups the isomorphism is essentially countable. Very recent work with Gao and Paolini shows that the relation 
$E_{ \ell_\infty}$ (coming from the quotient $R^N/ \ell_\infty$) is Borel reducible to the isomorphism relation for procountable nilpotent-2 groups.  In particular, the latter one is not classifiable by countable models (equivalently: it is not below the graph isomorphism).

---