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arXiv · 2512.12256

Procountable groups are not classifiable by countable structures

Su Gao·André Nies·Gianluca Paolini
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Abstract

We prove that topological isomorphism on procountable groups is not classifiable by countable structures, in the sense of descriptive set theory. In fact, the equivalence relation $\ell_\infty$ expressing that two sequences of reals have a bounded difference is Borel reducible to it. This marks substantial progress on an open problem of Kechris, Nies and Tent (2018): to determine the exact complexity of the isomorphism relation among all non-archimedean Polish groups.

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BibTeXRIS

Su Gao, André Nies, Gianluca Paolini. 2025-12-13. Procountable groups are not classifiable by countable structures. https://arxiv.org/abs/2512.12256

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