223 citations · 725 across the 95 of their papers we have counts for
10 papers · 1 filter
Inner models with large cardinal features usually obtained by forcing
Arthur Apter, Victoria Gitman, Joel David Hamkins
We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then t…
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…
The hierarchy of equivalence relations on the natural numbers under computable reducibility
Samuel Coskey, Joel David Hamkins, Russell Miller
The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computab…
The set-theoretic multiverse
Joel David Hamkins
The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-the…
Set-Theoretic Geology
Gunter Fuchs, Joel David Hamkins, Jonas Reitz
A ground of the universe V is a transitive proper class W subset V, such that W is a model of ZFC and V is obtained by set forcing over W, so that V = W[G] for some W-generic filte…
The Rigid Relation Principle, a New Weak Choice Principle
Joel David Hamkins, Justin Palumbo
The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigi…