Abstract
We present a characterization of supercompactness measures for $\omega_1$ in L($\mathbb{R}$), 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 $\mathsf{ZFC+AD}^{L\mathbb{R}}$, and the second proving the uniqueness of the supercompactness measure over $\mathcal{P}_{\omega_l }(\lambda)$ in L ($\mathbb{R}$) for $\lambda > \delta_1^2$.
Citation
Itay Neeman. "Inner models and ultrafilters in L($\mathbb{R})." Bull. Symbolic Logic 13 (1) 31 - 53, March 2007. https://doi.org/10.2178/bsl/1174668217
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