Grigor Sargsyan

collaborators

4 papers

math.LO2026

Ultrapowers of determinacy models as iteration trees on HOD

Gabriel Goldberg, Grigor Sargsyan, Benjamin Siskind

In the 1990s, Steel and Woodin showed that under large cardinal hypotheses, the HOD of $L (R)$ admits a fine-structural analysis. Although this theorem sheds light on variou…

math.LO2026

The failure of square at all uncountable cardinals is weaker than a Woodin limit of Woodin cardinals

Douglas Blue, Paul Larson, Grigor Sargsyan

We force the Axiom of Choice over the least initial segment of a Nairian model satisfying ZF. In the forcing extension, square_kappa fails at all uncountable cardinals kappa, and e…

math.LO2025

AD $^{+}$ implies that $I ¨ _{1}$ is a $I^$ -Berkeley cardinal

Douglas Blue, Grigor Sargsyan

Following \cite{bagaria2019large}, given cardinals $I^º < I^»$ , we say $I^º$ is a club $I^»$ -Berkeley cardinal if for every transitive set $N$ of size $< I^»$ such that $I^º \subseteq N$ , th…

math.LO2025

Nairian Models

Douglas Blue, Paul B. Larson, Grigor Sargsyan

We introduce a hierarchy of models of the Axiom of Determinacy called \emph{Nairian models}. Forcing over the simplest Nairian model, we obtain a model of ${\sf{ZFC}}+{\sf{MM^{++}}…

Ultrapowers of determinacy models as iteration trees on HOD

The failure of square at all uncountable cardinals is weaker than a Woodin limit of Woodin cardinals

AD+ implies that I¨1​ is a I^-Berkeley cardinal

Nairian Models

AD $^{+}$ implies that $I ¨ _{1}$ is a $I^$ -Berkeley cardinal