Gabriel Goldberg

Gabriel Goldberg is an Assistant Professor at the University of California, Berkeley, affiliated with the Group in Logic and the Methodology of Science. He works on set theory, large cardinals, inner model theory, and infinite combinatorics.

• Education: PhD in Mathematics (2019) and AB in Mathematics (2014) from Harvard University.

Goldberg's research explores the interplay between large cardinals, elementary embeddings, and the structure of HOD under the Ultrapower Axiom. His work addresses the equiconsistency of strongly compact and supercompact cardinals, periodicity in the cumulative hierarchy under choiceless axioms, and the uniqueness of elementary embeddings. He has co-organized the 2025 inner model theory conference at UC Berkeley.

Recent publications focus on the Galvin property, reflecting measures, and constraints on cardinal-preserving embeddings. Under the Ultrapower Axiom, he investigates implications for the Generalized Continuum Hypothesis and the structure of extender embeddings.

• Scientific Awards: Sacks Prize (2019) for his dissertation on the Ultrapower Axiom, European Set Theory Plenary Speaker (2019), and Harvard Distinction in Teaching Award (2018).

Goldberg's teaching includes courses at UC Berkeley (Math 236, 113) and Harvard (Math 99r, CS 20, 121, CSCI E-250). He serves as a referee for journals like the Journal of Symbolic Logic and Archive for Mathematical Logic.