Work

Hilbert Spaces Admit No Nontrivial Finitary Discrete Imaginaries

Year: 2026

Type: article

Abstract: We prove that every functor from the category of Hilbert spaces and linear isometric embeddings to the category of sets which preserves directed colimits must be essentially constant on all infinite-dimensional spaces. In other words, every finitary set-valued imaginary over the theory of Hilbert spaces, in a broad signature-independent sense, must be essentially trivial. This extends a result and answers a question by Lieberman–Rosický–Vasey, who showed that no such functor on the supercategory of Hilbert spaces and injective linear contractions can be faithful.

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2026.10192

Authors: RUIYUAN CHEN, ISABEL TRINDADE

Institutions: University of Warsaw, University of Amsterdam

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: National Science Foundation