Jan Mycielski and H. Steinhaus. A mathematical axiom contradicting the axiom of choice. Bulletin de l'Académie Polonaise des Sciences, Série des sciences mathématiques, astronomiques et physiques, vol. 10 (1962), pp. 1–3. - Jan Mycielski. On the axiom of determinateness. Fundamenta mathematicae, vol. 53 (1964), pp. 205–224. - Jan Mycielski and S. Świerczkowski. On the Lebesgue measurability and the axiom of determinateness. Fundamenta mathematicae, vol. 54 (1964), pp. 67–71. - Jan Mycielski. On the axiom of determinateness (II). Fundamenta mathematicae, vol. 59 (1966), pp. 203–212.

James E. Baumgartner

doi:10.2307/2271562

Jan Mycielski and H. Steinhaus. A mathematical axiom contradicting the axiom of choice. Bulletin de l'Académie Polonaise des Sciences, Série des sciences mathématiques, astronomiques et physiques, vol. 10 (1962), pp. 1–3. - Jan Mycielski. On the axiom of determinateness. Fundamenta mathematicae, vol. 53 (1964), pp. 205–224. - Jan Mycielski and S. Świerczkowski. On the Lebesgue measurability and the axiom of determinateness. Fundamenta mathematicae, vol. 54 (1964), pp. 67–71. - Jan Mycielski. On the axiom of determinateness (II). Fundamenta mathematicae, vol. 59 (1966), pp. 203–212.

Journal of Symbolic Logic ◽

10.2307/2271562 ◽

1971 ◽

Vol 36 (1) ◽

pp. 164-166

Author(s):

James E. Baumgartner

Keyword(s):

Axiom Of Choice ◽

Lebesgue Measurability ◽

The Axiom Of Choice

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The Axiom of Choice Machine

10.1093/oso/9780198810339.003.0006 ◽

2018 ◽

Author(s):

Alexander R. Pruss

Keyword(s):

Set Theory ◽

Laws Of Nature ◽

Axiom Of Choice ◽

Dutch Book ◽

The Axiom Of Choice

This is a mainly technical chapter concerning the causal embodiment of the Axiom of Choice from set theory. The Axiom of Choice powered a construction of an infinite fair lottery in Chapter 4 and a die-rolling strategy in Chapter 5. For those applications to work, there has to be a causally implementable (though perhaps not compatible with our laws of nature) way to implement the Axiom of Choice—and, for our purposes, it is ideal if that involves infinite causal histories, so the causal finitist can reject it. Such a construction is offered. Moreover, other paradoxes involving the Axiom of Choice are given, including two Dutch Book paradoxes connected with the Banach–Tarski paradox. Again, all this is argued to provide evidence for causal finitism.

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