On The Derived Models Of Self-Iterable Universes

Takehiko Gappo, Grigor Sargsyan

Research output: Contribution to journalArticlepeer-review


We show that if the universe is self-iterable and k is an inaccessible limit of Woodin cardinal then ADR+Φ is regular" holds in the derived model at k. The proof is fine-structure free, and only assumes basic knowledge of iteration trees and iteration strategies. Our proof can be viewed as the finestructure free version of the well-known fact that ADR+Φ is regular" is true in the derived models of hod mice that have inaccessible limit ofWoodin 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.

Original languageEnglish (US)
Pages (from-to)1321-1329
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number3
StatePublished - 2022

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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