Journal of Symbolic Logic 74 (1):315-335 (2009)

Authors
Jack Steel
University of Edinburgh
Abstract
We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal k ≥ N₃ such that □k and □(k) fail. 2) There is a cardinal k such that k is weakly compact in the generic extension by Col(k, k⁺). Of special interest is 1) with k = N₃ since it follows from PFA by theorems of Todorcevic and Velickovic. Our main new technical result, which is due to the first author, is a weak covering theorem for the model obtained by stacking mice over $K^c ||k.$
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DOI 10.2178/jsl/1231082314
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References found in this work BETA

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Combinatorial Principles in the Core Model for One Woodin Cardinal.Ernest Schimmerling - 1995 - Annals of Pure and Applied Logic 74 (2):153-201.
Characterization of □Κin Core Models.Ernest Schimmerling & Martin Zeman - 2004 - Journal of Mathematical Logic 4 (01):1-72.
A Criterion for Coarse Iterability.Gunter Fuchs, Itay Neeman & Ralf Schindler - 2010 - Archive for Mathematical Logic 49 (4):447-467.

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Citations of this work BETA

Indestructible Strong Unfoldability.Joel David Hamkins & Thomas A. Johnstone - 2010 - Notre Dame Journal of Formal Logic 51 (3):291-321.
The Combinatorial Essence of Supercompactness.Christoph Weiß - 2012 - Annals of Pure and Applied Logic 163 (11):1710-1717.
Descriptive Inner Model Theory.Grigor Sargsyan - 2013 - Bulletin of Symbolic Logic 19 (1):1-55.
Combinatorial Dichotomies in Set Theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.

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