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ZF + “Every set is the same size as a wellfounded set”

Published online by Cambridge University Press:  12 March 2014

Thomas Forster
Thomas Forster*
Affiliation:
Centre for Mathematical Sciences, Wilberforce RD Cambridge CB3 0WB, England, E-mail: [email protected]
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Abstract

Let ZFB be ZF + “every set is the same size as a wellfounded set”. Then the following are true.

Every sentence true in every (Rieger-Bernays) permutation model of a model of ZF is a theorem of ZFB. (i.e., ZFB is the theory of Rieger-Bernays permutation models of models of ZF) ZF and ZFAFA are both extensions of ZFB conservative for stratified formulæ. The class of models of ZFB is closed under creation of Rieger-Bernays permutation models.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 1 , March 2003 , pp. 1 - 4
Copyright
Copyright © Association for Symbolic Logic 2003

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References

REFERENCES

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