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The present paper is concerned with the relation between recurrence axioms and Laver-generic large cardinal axioms in light of principles of generic absoluteness and the Ground Axiom. M. Viale proved that Martin's Maximum$^{++}$ together with the ass
Externí odkaz:
http://arxiv.org/abs/2410.15384
We show that in the $\mathbb{P}_{\max}$ extension of a certain Chang-type model of determinacy, if $\kappa\in\{\omega_1, \omega_2, \omega_3\}$, then the restriction of the club filter on $\kappa\cap\mathrm{Cof}(\omega)$ to HOD is an ultrafilter in HO
Externí odkaz:
http://arxiv.org/abs/2307.13682
Based on earlier work of the third author, we construct a Chang-type model with supercompact measures extending a derived model of a given hod mouse with a regular cardinal $\delta$ that is both a limit of Woodin cardinals and a limit of ${<}\delta$-
Externí odkaz:
http://arxiv.org/abs/2307.08607
Autor:
Gappo, Takehiko, Sargsyan, Grigor
Assuming the existence of a certain hod pair with a Woodin cardinal that is a limit of Woodin cardinals, we show that the Chang model satisfies $\mathsf{AD}^+$ in any set generic extensions.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2302.06487
Autor:
Sargsyan, Grigor, Gappo, Takehiko
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 ite
Externí odkaz:
http://arxiv.org/abs/2111.06455
Akademický článek
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Autor:
Gappo, Takehiko
Publikováno v:
Bulletin of Symbolic Logic; Jun2024, Vol. 30 Issue 2, p279-282, 4p
Autor:
Gappo, Takehiko
We study determinacy from the perspective of inner model theory. In this thesis, there are three main results and all of them claim that there is a model of some strong determinacy axiom. Firstly, we show that if V is self-iterable and has inaccessib
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e5e12c000874fd10c2ddebfa0a40a83e
Akademický článek
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Autor:
Aksornthong, Navin1 (AUTHOR) navin.aksornthong@rutgers.edu, Gappo, Takehiko2 (AUTHOR) takehiko.gappo@tuwien.ac.at, Holland, James3 (AUTHOR) jch258@scarletmail.rutgers.edu, Sargsyan, Grigor4 (AUTHOR) gsargsyan@impan.pl
Publikováno v:
Journal of Mathematical Logic. Oct2024, p1. 1p.