Homogeneous changes in cofinalities with applications to HOD

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Journal of Mathematical Logic 17 (2):1750007 (2017)
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Abstract

We present a new technique for changing the cofinality of large cardinals using homogeneous forcing. As an application we show that many singular cardinals in [Formula: see text] can be measurable in HOD. We also answer a related question of Cummings, Friedman and Golshani by producing a model in which every regular uncountable cardinal [Formula: see text] in [Formula: see text] is [Formula: see text]-supercompact in HOD.

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10.1142/s0219061317500076

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Citations of this work

A Mathias criterion for the Magidor iteration of Prikry forcings.Omer Ben-Neria - 2023 - Archive for Mathematical Logic 63 (1):119-134.
Approachable free subsets and fine structure derived scales.Dominik Adolf & Omer Ben-Neria - 2024 - Annals of Pure and Applied Logic 175 (7):103428.

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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.
Forcing closed unbounded sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Collapsing the cardinals of HOD.James Cummings, Sy David Friedman & Mohammad Golshani - 2015 - Journal of Mathematical Logic 15 (2):1550007.
On closed unbounded sets consisting of former regulars.Moti Gitik - 1999 - Journal of Symbolic Logic 64 (1):1-12.

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