Condensed Sets and the Solovay Model

Nathaniel Bannister; Dianthe Basak

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arXiv · 2602.09283

Condensed Sets and the Solovay Model

Nathaniel Bannister·Dianthe Basak

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Abstract

We exhibit a geometric morphism from the Grothendieck topos representing the Solovay model to the $\kappa$-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.

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BibTeX RIS

Nathaniel Bannister, Dianthe Basak. 2026-02-09. Condensed Sets and the Solovay Model. https://arxiv.org/abs/2602.09283

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