Inner models and ultrafilters in l(r)

Bulletin of Symbolic Logic 13 (1):31-53 (2007)
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Abstract

We present a characterization of supercompactness measures for ω1 in L(R), and of countable products of such measures, using inner models. We give two applications of this characterization, the first obtaining the consistency of $\delta_3^1 = \omega_2$ with $ZFC+AD^{L(R)}$ , and the second proving the uniqueness of the supercompactness measure over ${\cal P}_{\omega_1} (\lambda)$ in L(R) for $\lambda > \delta_1^2$

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Citations of this work

An inner model theoretic proof of Becker’s theorem.Grigor Sargsyan - 2019 - Archive for Mathematical Logic 58 (7-8):999-1003.

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References found in this work

The Core Model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
Inner Models with Many Woodin Cardinals.J. R. Steel - 1993 - Annals of Pure and Applied Logic 65 (2):185-209.
Sets Constructed From Sequences of Measures: Revisited.William J. Mitchell - 1983 - Journal of Symbolic Logic 48 (3):600-609.
On the Determinacy of Games on Ordinals.L. A. Harrington - 1981 - Annals of Mathematical Logic 20 (2):109.
AD and the Supercompactness of ℵ1.Howard Becker - 1981 - Journal of Symbolic Logic 46 (4):822-842.

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