Eyal Kaplan

About Me

I am a postdoctoral researcher in mathematics at UC Berkeley, working with Gabe Goldberg. My research interests lie in set theory—particularly forcing, large cardinals, and inner model theory. I completed my PhD in Tel-Aviv university under the supervision of Moti Gitik.

You can reach me at: eyalkaplan 'at' berkeley.edu.

Publications and Preprints

The number of normal measures, revisited 2025. [pdf]

A Kunen-like model with a critical failure of the Continuum Hypothesis with Omer Ben-Neria, 2025. [pdf]

On fresh sets in iterations of Prikry-type forcing notions with Moti Gitik, Accepted, Israel Journal of Mathematics, 2025. [pdf]

The potentialist principle with Omer Ben-Neria and Gabe Goldberg, Advances in Mathematics, 2025. [pdf]

The Magidor iteration and restrictions of ultrapowers to the ground model Israel Journal of Mathematics, 2024. [pdf]

On Easton support iteration of Prikry type forcing notions with Moti Gitik, JSL, 2023. [pdf]

Non-stationary support iterations of Prikry forcings and restrictions of ultrapower embeddings to the ground model with Moti Gitik, Annals of Pure and Applied Logic, 2023 [pdf]

On restrictions of ultrafilters from generic extensions to ground models with Moti Gitik, JSL, 2022 [pdf]

Non-homogeneity of quotients of Prikry forcings with Moti Gitik, Archive for Mathematical Logic, 2019 [pdf]

Slides

Applications of the fusion technique, Berkeley Inner model theory conference, 2025. [slides]
Failure of GCH on a measurable with the Ultrapower Axiom, European set theory conference, 2024. [slides]