14 citations · 17 across the 4 of their papers we have counts for
5 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…
Strongly uplifting cardinals and the boldface resurrection axioms
Joel David Hamkins, Thomas A. Johnstone
We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost hugely unfoldable ca…
On ground model definability
Victoria Gitman, Thomas A. Johnstone
Laver, and Woodin independently, showed that models of are uniformly definable in their set-forcing extensions, using a ground model parameter. We investigate ground mo…
Resurrection axioms and uplifting cardinals
Joel David Hamkins, Thomas A. Johnstone
We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances of the resurrection…
What is the theory ZFC without power set?
Victoria Gitman, Joel David Hamkins, Thomas A. Johnstone
We show that the theory ZFC-, consisting of the usual axioms of ZFC but with the power set axiom removed-specifically axiomatized by extensionality, foundation, pairing, union, inf…