Condensed Sets and the Solovay Model

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Nathaniel Bannister, Dianthe Basak
DOI: 10.48550/arxiv.2602.09283
Cited by: 0

Abstract

We exhibit a geometric morphism from the Grothendieck topos representing the Solovay model to the $κ$-pyknotic sets of Barwick--Haine and Clausen--Scholze. We then use the properties of this morphism and automatic continuity in the Solovay model to prove Clausen--Scholze's resolution of the Whitehead problem for discrete condensed abelian groups. We also exhibit an analogous internal $Ext$ computation between locally compact abelian groups in the Solovay model.

Fields of Study & Subjects

Homotopy and Cohomology in Algebraic Topology Advanced Topology and Set Theory Advanced Operator Algebra Research

Publication details

Journal / source
arXiv (Cornell University)
Publication date
9 February 2026
Language
EN
Document type
Preprint