Douglas Blue

collaborators

3 papers

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^{++}}…

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