6 citations · 16 across the 22 of their papers we have counts for
5 papers · 2 filters
Some combinatorial properties of Ultimate L and V
Gabriel Goldberg
This paper establishes a number of constraints on the structure of large cardinals under strong compactness assumptions. These constraints coincide with those imposed by the Ultrap…
The Ultrapower Axiom
Gabriel Goldberg
The inner model problem for supercompact cardinals, one of the central open problems in modern set theory, asks whether there is a canonical model of set theory with a supercompact…
Periodicity in the cumulative hierarchy
Gabriel Goldberg, Farmer Schlutzenberg
We investigate the structure of rank-to-rank elementary embeddings, working in ZF set theory without the Axiom of Choice. Recall that the levels of the cumulative hierarchy a…
Even ordinals and the Kunen inconsistency
Gabriel Goldberg
This paper contributes to the theory of large cardinals beyond the Kunen inconsistency, or choiceless large cardinal axioms, in the context where the Axiom of Choice is not assumed…
Structure theorems above a strongly compact cardinal
Gabriel Goldberg
While many inner model theoretic combinatorial principles are incompatible with large cardinal axioms, on some rare occasions, large cardinals actually imply that the structure of…