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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
Isomorphism Classes of Generating Sets
Tom Benhamou, James Cummings, Gabriel Goldberg +2
We introduce a new class of ultrafilters which generalizes the well-known class of simple -point ultrafilters. We prove that for any well-founded -directed partial order $\ma…
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…