### Stacking mice

Ronald Jensen, Ernest Schimmerling, Ralf Schindler, and John Steel
Source: J. Symbolic Logic Volume 74, Issue 1 (2009), 315-335.

#### 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 κ ≥ ℵ3 such that □κ and □(κ) fail. 2) There is a cardinal κ such that κ is weakly compact in the generic extension by Col(κ,κ+). Of special interest is 1) with κ = ℵ3 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 Kc || κ.

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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1231082314
Digital Object Identifier: doi:10.2178/jsl/1231082314
Mathematical Reviews number (MathSciNet): MR2499432
Zentralblatt MATH identifier: 1161.03031

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