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Article
Probability Axioms and Set Theory Paradoxes
Symmetry
  • Ari Herman
  • John Caughman, Portland State University
Document Type
Article
Publication Date
1-22-2021
Subjects
  • Set theory,
  • Probability,
  • Axiom of choice,
  • Paradoxes -- Mathematical models
Abstract

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.

Rights

© 2021 by the authors. Licensee MDPI, Basel, Switzerland.


This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI
10.3390/sym13020179
Persistent Identifier
https://archives.pdx.edu/ds/psu/34902
Citation Information
Herman, Ari; Caughman, John. (2021). "Probability Axioms and Set Theory Paradoxes" Symmetry 13, no. 2: 179.