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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 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
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^{++}}…