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arXiv · 2308.11826

Chain Conditions and the Axiom of Choice

Ilijas Farah·Jeffrey Marshall-Milne
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Abstract

Within the framework of Zermelo-Fraenkel set theory without the Axiom of Choice, we establish equivalents to the assertion "the union of a countable collection of finite sets is countable" in the context of metric spaces, probability theory, and Hilbert spaces. The categorical principle underlying these equivalences is identified.

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Ilijas Farah, Jeffrey Marshall-Milne. 2023-08-22. Chain Conditions and the Axiom of Choice. https://arxiv.org/abs/2308.11826

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