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Independence, Randomness and the Axiom of Choice

Michiel van Lambalgen
The Journal of Symbolic Logic
Vol. 57, No. 4 (Dec., 1992), pp. 1274-1304
DOI: 10.2307/2275368
Stable URL: http://www.jstor.org/stable/2275368
Page Count: 31
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Independence, Randomness and the Axiom of Choice
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Abstract

We investigate various ways of introducing axioms for randomness in set theory. The results show that these axioms, when added to ZF, imply the failure of AC. But the axiom of extensionality plays an essential role in the derivation, and a deeper analysis may ultimately show that randomness is incompatible with extensionality.

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