On the derived models of self iterable universes

Grigor Sargsyan; Takehiko Gappo

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arXiv · 2111.06455

On the derived models of self iterable universes

Grigor Sargsyan·Takehiko Gappo

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Abstract

We show that if the universe is self-iterable and $\kappa$ is an inaccessible limit of Woodin cardinal then $AD_R + "\Theta$ is regular" holds in the derived model at $\kappa$. The proof is fine-structure free, and only assumes basic knowledge of iteration trees and iteration strategies. Our proof can be viewed as the fine-structure free version of the well-known fact that $AD_R + "\Theta$ is regular" is true in the derived models of hod mice that have inaccessible limit of Woodin cardinals (see for example [6]). However, the proof uses a different set of ideas and is more general.

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Grigor Sargsyan, Takehiko Gappo. 2021-11-11. On the derived models of self iterable universes. https://arxiv.org/abs/2111.06455

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