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Regular embeddings of the stationary tower and Woodin's maximality theorem

Published online by Cambridge University Press:  12 March 2014

Richard Ketchersid ,
Paul B. Larson  and
Jindřich Zapletal
Richard Ketchersid
Affiliation:
Department of Mathematics, Miami University Oxford, Ohio 45056, USA. E-mail: ketchero@muohio.edu
Paul B. Larson
Affiliation:
Department of Mathematics, Miami University Oxford, Ohio 45056, USA. E-mail: larsonpb@muohio.edu
Jindřich Zapletal
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL 32611, USA. E-mail: zapletal@math.ufl.edu
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Abstract

We present Woodin's proof that if there exists a measurable Woodin cardinal δ then there is a forcing extension satisfying all sentences ϕ such that CH + ϕ holds in a forcing extension of V by a partial order in Vδ. We also use some of the techniques from this proof to show that if there exists a stationary limit of stationary limits of Woodin cardinals, then in a homogeneous forcing extension there is an elementary embedding j: V → M with critical point such that M is countably closed in the forcing extension.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010 , pp. 711 - 727
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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