Hilbert Spaces Without Countable AC

Bruce Blackadar; Ilijas Farah; Asaf Karagila

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arXiv · 2304.09602

Hilbert Spaces Without Countable AC

Bruce Blackadar·Ilijas Farah·Asaf Karagila

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Abstract

This article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot be said about Hilbert spaces and operators on them in ZF set theory without any assumptions of Choice axioms, even the CC. (2) We view Hilbert spaces as ``quantized'' sets and obtain some set-theoretic results from associated Hilbert spaces.

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BibTeX RIS

Bruce Blackadar, Ilijas Farah, Asaf Karagila. 2023-04-19. Hilbert Spaces Without Countable AC. https://arxiv.org/abs/2304.09602

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