Journal of Mathematical Logic 15 (2):1550007 (2015)

Assuming that GCH holds and [Formula: see text] is [Formula: see text]-supercompact, we construct a generic extension [Formula: see text] of [Formula: see text] in which [Formula: see text] remains strongly inaccessible and [Formula: see text] for every infinite cardinal [Formula: see text]. In particular the rank-initial segment [Formula: see text] is a model of ZFC in which [Formula: see text] for every infinite cardinal [Formula: see text].
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DOI 10.1142/s0219061315500075
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References found in this work BETA

Suitable Extender Models I.W. Hugh Woodin - 2010 - Journal of Mathematical Logic 10 (1):101-339.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
$K$ Without the Measurable.Ronald Jensen & John Steel - 2013 - Journal of Symbolic Logic 78 (3):708-734.
Radin Forcing and its Iterations.John Krueger - 2007 - Archive for Mathematical Logic 46 (3-4):223-252.

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More on HOD-Supercompactness.Arthur W. Apter, Shoshana Friedman & Gunter Fuchs - 2021 - Annals of Pure and Applied Logic 172 (3):102901.
Hod, V and the Gch.Mohammad Golshani - 2017 - Journal of Symbolic Logic 82 (1):224-246.

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