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March 2009 Stacking mice
Ronald Jensen, Ernest Schimmerling, Ralf Schindler, John Steel
J. Symbolic Logic 74(1): 315-335 (March 2009). DOI: 10.2178/jsl/1231082314

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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Ronald Jensen. Ernest Schimmerling. Ralf Schindler. John Steel. "Stacking mice." J. Symbolic Logic 74 (1) 315 - 335, March 2009. https://doi.org/10.2178/jsl/1231082314

Information

Published: March 2009
First available in Project Euclid: 4 January 2009

zbMATH: 1161.03031
MathSciNet: MR2499432
Digital Object Identifier: 10.2178/jsl/1231082314

Rights: Copyright © 2009 Association for Symbolic Logic

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Vol.74 • No. 1 • March 2009
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