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Successors of singular cardinals and measurability revisited

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter
Arthur W. Apter*
Affiliation:
Department of Mathematics, Baruch College, City University of New York, New York, New York 10010
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Extract

Before the remarkable theorem of Martin and Steel [6] showing that the existence of a supercompact cardinal κ implies L[R] ⊨ ZF + AD + DC, and the later theorem of Woodin [9] showing that Con(ZFC + There exists an ω sequence of Woodin cardinals) ⇔ Con(ZF + AD + DC), much set-theoretic research was focused upon showing that the consistency of fragments of AD + DC followed from more “reasonable” hypotheses such as versions of supercompactness. A good example of this is provided by the results of [1], in which the following theorems are proven.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 2 , June 1990 , pp. 492 - 501
Copyright
Copyright © Association for Symbolic Logic 1990

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References

REFERENCES

[1]Apter, A., Successors of singular cardinals and measurability, Advances in Mathematics, vol. 55 (1985), pp. 228–241.CrossRefGoogle Scholar
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[9]Woodin, H., unpublished.Google Scholar