Published In

Symmetry

Document Type

Article

Publication Date

1-22-2021

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.

Creative Commons License
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

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