Stacking mice

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

Jack Steel
University of Edinburgh

Citations of this work

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Equiconsistencies at subcompact cardinals.Itay Neeman & John Steel - 2016 - Archive for Mathematical Logic 55 (1-2):207-238.
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References found in this work

[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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