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The complexity of the core model

Published online by Cambridge University Press:  12 March 2014

William J. Mitchell
William J. Mitchell*
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611., USA. E-mail:[email protected]
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Abstract

If there is no inner model with a cardinal κ such that ο(κ) = κ++ then the set K ∩ Hω1 is definable over Hω1 by a Δ4 formula, and the set of countable initial segments of the core model is definable over Hω1 by a Π3 formula. We show that if there is an inner model with infinitely many measurable cardinals then there is a model in which is not definable Σ3 by any Σ3 formula, and K ∩ Hω1 is not definable by any boolean combination of Σ3 formulas.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1393 - 1398
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Mitchell, William J., The core model for sequences of measures, Mathematics Proceedings of the Cambridge Philosophical Society, vol. 95 (1984), pp. 41—58.CrossRefGoogle Scholar
[2] Mitchell, William J., Σ1 3 absoluteness for sequences of measures, Set theory of the continuum (Judah, H., Just, W., and Woodin, W. Hugh, editors), Springer-Verlag, Berlin, 1992, pp. 311—355.CrossRefGoogle Scholar
[3] Mitchell, William J. and Steel, John R., Fine structure and iteration trees, ASL Lecture Notes in Logic, vol. 3, Springer-Verlag, Berline, 1994.CrossRefGoogle Scholar
[4] Steel, John R., The core model iterahility problem, ASL Lecture Notes in Logic, vol. 8, Springer-Verlag, 1996.CrossRefGoogle Scholar