6 citations · 16 across the 22 of their papers we have counts for
7 papers · 1 filter
The internal relation
Gabriel Goldberg
This paper explores various generalizations of the Mitchell order focusing mostly on a generalization called the internal relation. The internal relation lacks the implicit strengt…
The Ultrapower Axiom and the equivalence between strong compactness and supercompactness
Gabriel Goldberg
The relationship between the large cardinal notions of strong compactness and supercompactness cannot be determined under the standard ZFC axioms of set theory. Under a hypothesis…
The Ultrapower Axiom implies GCH above a supercompact cardinal
Gabriel Goldberg
We prove that the Generalized Continuum Hypothesis holds above a supercompact cardinal assuming the Ultrapower Axiom, an abstract comparison principle motivated by inner model theo…
Fréchet cardinals
Gabriel Goldberg
An infinite cardinal is called Fréchet if the Fréchet filter on extends to a countably complete ultrafilter. We investigate the relationship between Fréchet cardinals and s…
The Rudin-Frolik order and the Ultrapower Axiom
Gabriel Goldberg
We study the structure of the Rudin-Frolik order on countably complete ultrafilters under the assumption that this order is directed. This assumption, called the Ultrapower Axiom,…
The seed order
Gabriel Goldberg
We study various orders on countably complete ultrafilters on ordinals that coincide and are wellorders under a hypothesis called the Ultrapower Axiom. Our main focus is on the rel…
Compactness and Comparison
Gabriel Goldberg
Assuming an abstract comparison principle called the Ultrapower Axiom, which is motivated by the comparison process of inner model theory and generalizes the statement that the Mit…