Measures in Nairian models, I

Gabriel Goldberg, Grigor Sargsyan

Assuming ${\mathrm{AD}}^{+}+V=L(P(\mathbb{R}))$, we show that the Ultrapower Axiom holds in ${\mathrm{HOD}}_s$ for every $\omega$-sequence of ordinals $s$. We use this result to analyze t…