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Limitations on the Fraenkel-Mostowski method of independence proofs

Published online by Cambridge University Press:  12 March 2014

Paul E. Howard
Paul E. Howard*
Affiliation:
Eastern Michigan University, Ypsilanti, Michigan 48197
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 3 , September 1973 , pp. 416 - 422
Copyright
Copyright © Association for Symbolic Logic 1973

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References

REFERENCES

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