964 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- City University of New YorkUS213 papers
- The Graduate Center, CUNYUS199 papers
- American Museum of Natural HistoryUS39 papers
- California Institute of TechnologyUS37 papers
- University of Massachusetts AmherstUS36 papers
- Princeton UniversityUS29 papers
- Space Telescope Science InstituteUS26 papers
- Centre National de la Recherche ScientifiqueFR18 papers
- Johns Hopkins UniversityUS17 papers
- Yale UniversityUS16 papers
- City College of New YorkUS15 papers
- Jet Propulsion LaboratoryUS15 papers
22 papers · 1 filter
Iteration theorems for subversions of forcing classes
Gunter Fuchs, Corey Bacal Switzer
We prove various iteration theorems for forcing classes related to subproper and subcomplete forcing, introduced by Jensen. In the first part, we use revised countable support iter…
Separating diagonal stationary reflection principles
Gunter Fuchs, Chris Lambie-Hanson
We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationsh…
Aronszajn tree preservation and bounded forcing axioms
Gunter Fuchs
I investigate the relationships between three hierarchies of reflection principles for a forcing class : the hierarchy of bounded forcing axioms, of -absoluteness and of…
Inner-model reflection principles
Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs +3
We introduce and consider the inner-model reflection principle, which asserts that whenever a statement in the first-order language of set theory is true in the set-theoreti…
A model of the generic Vopěnka principle in which the ordinals are not Mahlo
Victoria Gitman, Joel David Hamkins
The generic Vopěnka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vopěnka scheme is relatively consistent with the ordinal…
Computable quotient presentations of models of arithmetic and set theory
Michał Tomasz Godziszewski, Joel David Hamkins
We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory. Specifically, no nonstandard model…
Small Forcing Makes Any Cardinal Superdestructible
Joel David Hamkins
Small forcing always ruins the indestructibility of an indestructible supercompact cardinal. In fact, after small forcing, any cardinal becomes superdestructible---any further…
Destruction or Preservation As You Like It
Joel David Hamkins
The Gap Forcing Theorem, a key contribution of this paper, implies essentially that after any reverse Easton iteration of closed forcing, such as the Laver preparation, every super…
Set-theoretic mereology
Joel David Hamkins, Makoto Kikuchi
We consider a set-theoretic version of mereology based on the inclusion relation and analyze how well it might serve as a foundation of mathematics. After establishing…
Large cardinals need not be large in HOD
Yong Cheng, Sy-David Friedman, Joel David Hamkins
We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal need not be weakly compact in HOD, and there c…
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…
Moving up and down in the generic multiverse
Joel David Hamkins, Benedikt Löwe
We give a brief account of the modal logic of the generic multiverse, which is a bimodal logic with operators corresponding to the relations "is a forcing extension of" and "is a g…
Structural connections between a forcing class and its modal logic
Joel David Hamkins, George Leibman, Benedikt Löwe
The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and p…
Every countable model of set theory embeds into its own constructible universe
Joel David Hamkins
The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. I…
Is the dream solution to the continuum hypothesis attainable?
Joel David Hamkins
The dream solution of the continuum hypothesis (CH) would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set…
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…
Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals
Samuel Coskey, Joel David Hamkins
We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite…
Exactly controlling the non-supercompact strongly compact cardinals
Arthur W. Apter, Joel David Hamkins
We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many c…
Changing the heights of automorphism towers
Joel David Hamkins, Simon Thomas
If is a centreless group, then denotes the height of the automorphism tower of . We prove that it is consistent that for every cardinal and every ordinal ,…