19 citations · 57 across the 23 of their papers we have counts for
25 papers · 1 filter
Class choice and the surprising weakness of Kelley-Morse set theory
Victoria Gitman, Joel David Hamkins, Thomas A. Johnstone
Kelley-Morse set theory KM is weaker than generally supposed and fails to prove several principles that may be desirable in a foundational second-order set theory. Even though KM i…
Between Ramsey and measurable cardinals
Victoria Gitman, Philipp Schlicht
We study several intertwined hierarchies between -Ramsey cardinals and measurable cardinals to illuminate the structure of the large cardinal hierarchy in this region. In partic…
ZFC without power set II: Reflection strikes back
Victoria Gitman, Richard Matthews
The theory ZFC implies the scheme that for every cardinal we can make many dependent choices over any definable relation without terminal nodes. Friedman, the first author,…
Model Theoretic Characterizations of Large Cardinals Revisited
Will Boney, Stamatis Dimopoulos, Victoria Gitman +1
In [Bon20], model theoretic characterizations of several established large cardinal notions were given. We continue this work, by establishing such characterizations for Woodin car…
The Virtual Large Cardinal Hierarchy
Stamatis Dimopoulos, Victoria Gitman, Dan Saattrup Nielsen
We continue the study of the virtual large cardinal hierarchy by analysing virtual versions of superstrong, Woodin, and Berkeley cardinals. Gitman and Schindler showed that virtual…
Structural Properties of the Stable Core
Sy-David Friedman, Victoria Gitman, Sandra Müller
The stable core, an inner model of the form for a simply definable predicate , was introduced by the first author in [Fri12], where he showed that $…