Inner mantles and iterated HOD

Jonas Reitz; Kameryn J Williams

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arXiv · 1810.08702

Inner mantles and iterated HOD

Jonas Reitz·Kameryn J Williams

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Abstract

We present a class forcing notion $\mathbb M(\eta)$, uniformly definable for ordinals $\eta$, which forces the ground model to be the $\eta$-th inner mantle of the extension, in which the sequence of inner mantles has length at least $\eta$. This answers a conjecture of Fuchs, Hamkins, and Reitz [FHR15] in the positive. We also show that $\mathbb M(\eta)$ forces the ground model to be the $\eta$-th iterated HOD of the extension, where the sequence of iterated HODs has length at least $\eta$. We conclude by showing that the lengths of the sequences of inner mantles and of iterated HODs can be separated to be any two ordinals you please.

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BibTeX RIS

Jonas Reitz, Kameryn J Williams. 2018-10-19. Inner mantles and iterated HOD. https://arxiv.org/abs/1810.08702

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