On the derived models of self-iterable universes

Gappo, Takehiko; Sargsyan, Grigor

doi:10.1090/proc/15741

On the derived models of self-iterable universes
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by Takehiko Gappo and Grigor Sargsyan PDF

Proc. Amer. Math. Soc. 150 (2022), 1321-1329 Request permission

Abstract:

We show that if the universe is self-iterable and $\kappa$ is an inaccessible limit of Woodin cardinal then $\mathsf {AD}_{\mathbb {R}}+“\Theta$ 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 $\mathsf {AD}_{\mathbb {R}}+“\Theta$ is regular” is true in the derived models of hod mice that have inaccessible limit of Woodin cardinals (see for example Sargsyan [Mem. Amer. Math. Soc. 236 (2015), p. viii+172]). However, the proof uses a different set of ideas and is more general.

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