## Journal of Symbolic Logic

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

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 18 March 2010

https://projecteuclid.org/euclid.jsl/1268917500

Digital Object Identifier
doi:10.2178/jsl/1268917500

Mathematical Reviews number (MathSciNet)
MR2648161

Zentralblatt MATH identifier
1192.03033

#### Citation

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. https://projecteuclid.org/euclid.jsl/1268917500.