Consistency strength of higher chang’s conjecture, without CH

Archive for Mathematical Logic 50 (7-8):759-775 (2011)
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Abstract

We prove that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\omega_3, \omega_2) \twoheadrightarrow (\omega_2, \omega_1)}$$\end{document} implies there is an inner model with a weak repeat measure.

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10.1007/s00153-011-0247-6

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References found in this work

Adding closed cofinal sequences to large cardinals.Lon Berk Radin - 1982 - Annals of Mathematical Logic 22 (3):243.
On successors of Jónsson cardinals.J. Vickers & P. D. Welch - 2000 - Archive for Mathematical Logic 39 (6):465-473.

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