Independence, randomness and the axiom of choice

Journal of Symbolic Logic 57 (4):1274-1304 (1992)
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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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10.2307/2275368

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Michiel Van Lambalgen
University of Amsterdam

Citations of this work

Representation and Invariance of Scientific Structures.Patrick Suppes - 2002 - CSLI Publications (distributed by Chicago University Press).
A Simple Logic of Functional Dependence.Alexandru Baltag & Johan van Benthem - 2021 - Journal of Philosophical Logic 50 (5):939-1005.
Russell's typicality as another randomness notion.Athanassios Tzouvaras - 2020 - Mathematical Logic Quarterly 66 (3):355-365.
What new axioms could not be.Kai Hauser - 2002 - Dialectica 56 (2):109–124.

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References found in this work

Philosophy of Mathematics.Paul Benacerraf & Hilary Putnam - 1985 - Philosophy of Science 52 (3):488-489.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):461-461.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Mathematical Logic Quarterly 24 (25‐30):461-461.
Traditional Cavalieri principles applied to the modern notion of area.John C. Simms - 1989 - Journal of Philosophical Logic 18 (3):275 - 314.

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