3 papers
math.LO2025
On Absoluteness Between V and HOD
Gabriel Goldberg, Dan Hathaway
We put together Woodin's basis theorem of AD and Vopěnka's theorem to conclude the following: If there is a proper class of Woodin cardinals, then every $(Σ^2_1)^{\mbox…
math.LO2025
Measures that violate the Generalized Continuum Hypothesis
Tom Benhamou, Gabriel Goldberg
A simple \(P_λ\)-point on a regular cardinal \(κ\) is a uniform ultrafilter on \(κ\) with a mod-bounded decreasing generating sequence of length \(λ\). We prove that if there is a…
math.LO2024
On the optimality of the HOD dichotomy
Gabriel Goldberg, Jonathan Osinski, Alejandro Poveda
In the first part of the manuscript, we establish several consistency results concerning Woodin's $\HOD$ hypothesis and large cardinals around the level of extendibility. First, we…