2 citations · 6 across the 11 of their papers we have counts for
21 papers · 1 filter
Choiceless cardinals and the continuum problem
Gabriel Goldberg
Under large cardinal hypotheses beyond the Kunen inconsistency -- hypotheses so strong as to contradict the Axiom of Choice -- we solve several variants of the generalized continuu…
Reinhardt cardinals in inner models
Gabriel Goldberg
A cardinal is weakly Reinhardt if it is the critical point of an elementary embedding from the universe of sets into a model that contains the double powerset of every ordinal. Thi…
Strongly compact cardinals and ordinal definability
Gabriel Goldberg
This paper explores several topics related to Woodin's HOD conjecture. We improve the large cardinal hypothesis of Woodin's HOD dichotomy theorem from an extendible cardinal to a s…
Measurable cardinals and choiceless axioms
Gabriel Goldberg
We prove that if there is an elementary embedding from the universe to itself, then there is a proper class of measurable successor cardinals.
A note on cardinal preserving embeddings
Gabriel Goldberg
We prove the consistency of the theory ZFC + there is a strongly compact cardinal from the existence of a cardinal preserving embedding from the universe into an inner model. The p…
A note on Woodin's HOD dichotomy
Gabriel Goldberg
A version of Woodin's HOD dichotomy is proved assuming the existence of just one strongly compact cardinal.