In this paper, we show that Zermelo–Fraenkel set theory with Choice (ZFC) conflicts with basic intuitions about randomness. Our background assumptions are the Zermelo–Fraenekel axioms without Choice (ZF) together with a fragment of Kolmogorov’s probability theory. Using these minimal assumptions, we prove that a weak form of Choice contradicts two common sense assumptions about probability—both based on simple notions of symmetry and independence.
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Locate the Document
Herman, Ari; Caughman, John. (2021). "Probability Axioms and Set Theory Paradoxes" Symmetry 13, no. 2: 179.