Condensed Sets and the Solovay Model
Logic
2026-02-24 v2 Category Theory
Abstract
We exhibit a geometric morphism from the Grothendieck topos representing the Solovay model to the -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 computation between locally compact abelian groups in the Solovay model.
Cite
@article{arxiv.2602.09283,
title = {Condensed Sets and the Solovay Model},
author = {Nathaniel Bannister and Dianthe Basak},
journal= {arXiv preprint arXiv:2602.09283},
year = {2026}
}
Comments
43 pages; comments welcome! The earlier proof of proposition 3.9 contained an error, the claim has thus been weakened to lemma B.3