223 citations · 725 across the 95 of their papers we have counts for
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The Rearrangement Number
Andreas Blass, Jörg Brendle, Will Brian +3
How many permutations of the natural numbers are needed so that every conditionally convergent series of real numbers can be rearranged to no longer converge to the same sum? We de…
ZFC proves that the class of ordinals is not weakly compact for definable classes
Ali Enayat, Joel David Hamkins
We prove that the class of all ordinals Ord is not weakly compact with respect to definable classes. Specifically, in any model of ZFC, the definable tree property fails for Ord, i…
The Ground Axiom
Joel David Hamkins
The ground axiom is the assertion that the set-theoretic universe is not obtainable by forcing over any inner model. Although this appears at first to be a second-order assertion,…
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…
The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme
Joel David Hamkins
The Vopěnka principle, which asserts that every proper class of first-order structures in a common language admits an elementary embedding between two of its members, is not equiva…