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Canonical seeds and Prikry trees

Published online by Cambridge University Press:  12 March 2014

Joel David Hamkins
Joel David Hamkins*
Affiliation:
Mathematics 15-215, City University of New York, CSI, 2800 Victory Blvd., Staten Island, NY 10314, USA, E-mail: hamkins@integral.math.csi.cuny.edu
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Abstract

Applying the seed concept to Prikry tree forcing ℙμ, I investigate how well ℙμ preserves the maximality property of ordinary Prikry forcing and prove that ℙμ, Prikry sequences are maximal exactly when μ admits no non-canonical seeds via a finite iteration. In particular, I conclude that if μ is a strongly normal supercompactness measure, then ℙμ Prikry sequences are maximal, thereby proving, for a large class of measures, a conjecture of W. Hugh Woodin's.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 2 , June 1997 , pp. 373 - 396
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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