Journal of Symbolic Logic

Limitations on the Fraenkel-Mostowski Method of Independence Proofs

Paul E. Howard

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Abstract

The Fraenkel-Mostowski method has been widely used to prove independence results among weak versions of the axiom of choice. In this paper it is shown that certain statements cannot be proved by this method. More specifically it is shown that in all Fraenkel-Mostowski models the following hold: 1. The axiom of choice for sets of finite sets implies the axiom of choice for sets of well-orderable sets. 2. The Boolean prime ideal theorem implies a weakened form of Sikorski's theorem.

Article information

Source
J. Symbolic Logic, Volume 38, Issue 3 (1973), 416-422.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183738753

Mathematical Reviews number (MathSciNet)
MR381989

Zentralblatt MATH identifier
0325.02043

JSTOR
links.jstor.org

Citation

Howard, Paul E. Limitations on the Fraenkel-Mostowski Method of Independence Proofs. J. Symbolic Logic 38 (1973), no. 3, 416--422. https://projecteuclid.org/euclid.jsl/1183738753


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