Gabriel Goldberg

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20242026

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math.LO2026

Measures in Nairian models, I

Gabriel Goldberg, Grigor Sargsyan

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

math.LO2026

Compactness phenomena in HOD and the Optimality of Magidor's Covering theorem

Tom Benhamou, James Cummings, Yair Hayut +2

We continue the study of compactness phenomena between the set-theoretic universe and $HOD$ initiated by Goldberg--Poveda \cite{GolPov}. We focus on compactness phenomena…

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…