Collapsing the cardinals of HOD

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

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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Citations of this work

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

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References found in this work

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.
Adding closed cofinal sequences to large cardinals.Lon Berk Radin - 1982 - Annals of Mathematical Logic 22 (3):243.

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