On The Derived Models Of Self-Iterable Universes

Takehiko Gappo; Grigor Sargsyan

doi:https://doi.org/10.1090/proc/15741

On The Derived Models Of Self-Iterable Universes

Takehiko Gappo, Grigor Sargsyan

School of Arts and Sciences, Mathematics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English (US)
Pages (from-to)	1321-1329
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	3
DOIs	https://doi.org/10.1090/proc/15741
State	Published - 2022

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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title = "On The Derived Models Of Self-Iterable Universes",

abstract = "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.",

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note = "Funding Information: Received by the editors January 28, 2020, and, in revised form, May 25, 2021. 2020 Mathematics Subject Classification. Primary 03E55, 03E60, 03E35. The second author{\textquoteright}s work was supported by the NSF Career Award DMS-1352034 and NSF Award DMS-1954149. Publisher Copyright: {\textcopyright} 2022 American Mathematical Society. All rights reserved.",

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AU - Sargsyan, Grigor

N1 - Funding Information: Received by the editors January 28, 2020, and, in revised form, May 25, 2021. 2020 Mathematics Subject Classification. Primary 03E55, 03E60, 03E35. The second author’s work was supported by the NSF Career Award DMS-1352034 and NSF Award DMS-1954149. Publisher Copyright: © 2022 American Mathematical Society. All rights reserved.

PY - 2022

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N2 - 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.

AB - 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.

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On The Derived Models Of Self-Iterable Universes

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