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arXiv · 1601.03482

Collapsing the cardinals of $HOD$

James Cummings·Sy David Friedman·Mohammad Golshani
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Abstract

Assuming that $GCH$ holds and $\kappa$ is $\kappa^{+3}$-supercompact, we construct a generic extension $W$ of $V$ in which $\kappa$ remains strongly inaccessible and $(\alpha^+)^{HOD} < \alpha^+$ for every infinite cardinal $\alpha < \kappa$. In particular the rank-initial segment $W_\kappa$ is a model of ZFC in which $(\alpha^+)^{HOD} < \alpha^+$ for every infinite cardinal $\alpha$.

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James Cummings, Sy David Friedman, Mohammad Golshani. 2016-01-14. Collapsing the cardinals of $HOD$. https://doi.org/10.1142/s0219061315500075

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