Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 38, Issue 3 (1973), 416-422.
Limitations on the Fraenkel-Mostowski Method of Independence Proofs
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.
J. Symbolic Logic, Volume 38, Issue 3 (1973), 416-422.
First available in Project Euclid: 6 July 2007
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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