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Chain Conditions and the Axiom of Choice (2308.11826v1)
Published 22 Aug 2023 in math.LO
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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