223 citations · 725 across the 95 of their papers we have counts for
7 papers · 1 filter
Satisfaction is not absolute
Joel David Hamkins, Ruizhi Yang
We prove that the satisfaction relation of first-order logic is not absolute between models of set theory having the structure and the f…
The foundation axiom and elementary self-embeddings of the universe
Ali Sadegh Daghighi, Mohammad Golshani, Joel David Hamkins +1
We consider the role of the foundation axiom and various anti-foundation axioms in connection with the nature and existence of elementary self-embeddings of the set-theoretic unive…
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…
Superstrong and other large cardinals are never Laver indestructible
Joan Bagaria, Joel David Hamkins, Konstantinos Tsaprounis +1
Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-exten…
The least weakly compact cardinal can be unfoldable, weakly measurable and nearly -supercompact
Brent Cody, Moti Gitik, Joel David Hamkins +1
We prove from suitable large cardinal hypotheses that the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly -supercompact, for any desired .…
Algebraicity and implicit definability in set theory
Joel David Hamkins, Cole Leahy
We analyze the effect of replacing several natural uses of definability in set theory by the weaker model-theoretic notion of algebraicity. We find, for example, that the class of…