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.
ASJC Scopus subject areas
- Applied Mathematics