Chain Conditions and the Axiom of Choice

Published 22 Aug 2023 in math.LO | (2308.11826v1)

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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