Journal of Symbolic Logic

Regular embeddings of the stationary tower and Woodin's Σ22 maximality theorem

Richard Ketchersid, Paul B. Larson, and Jindřich Zapletal

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We present Woodin's proof that if there exists a measurable Woodin cardinal δ, then there is a forcing extension satisfying all Σ22 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 ω1V such that M is countably closed in the forcing extension.

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J. Symbolic Logic Volume 75, Issue 2 (2010), 711-727.

First available in Project Euclid: 18 March 2010

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Ketchersid, Richard; Larson, Paul B.; Zapletal, Jindřich. Regular embeddings of the stationary tower and Woodin's Σ 2 2 maximality theorem. J. Symbolic Logic 75 (2010), no. 2, 711--727. doi:10.2178/jsl/1268917500.

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