69 research outputs found
Strongly uplifting cardinals and the boldface resurrection axioms
We introduce the strongly uplifting cardinals, which are equivalently
characterized, we prove, as the superstrongly unfoldable cardinals and also as
the almost hugely unfoldable cardinals, and we show that their existence is
equiconsistent over ZFC with natural instances of the boldface resurrection
axiom, such as the boldface resurrection axiom for proper forcing.Comment: 24 pages. Commentary concerning this article can be made at
http://jdh.hamkins.org/strongly-uplifting-cardinals-and-boldface-resurrectio
A hierarchy of Ramsey-like cardinals
We introduce a hierarchy of large cardinals between weakly compact and
measurable cardinals, that is closely related to the Ramsey-like cardinals
introduced by Victoria Gitman, and is based on certain infinite filter games,
however also has a range of equivalent characterizations in terms of elementary
embeddings. The aim of this paper is to locate the Ramsey-like cardinals
studied by Gitman, and other well-known large cardinal notions, in this
hierarchy
- …