Resurrection axioms and uplifting cardinals

Resurrection axioms and uplifting cardinals

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 axioms are equiconsistent over ZFC with the existence of an uplifting car-

Large cardinals and resurrection axioms

Notes to “The Resurrection Axioms”

I will discuss a new class of forcing axioms, the Resurrection Axioms (RA), and the Weak Resurrection Axioms (wRA). While Cohen’s method of forcing has been designed to change truths about the set-theoretic universe you live in, the point of Resurrection is that some truths that have been changed by forcing can in fact be resurrected, i.e. forced to hold again. In this talk, I will illustrate h...

Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtai...

The Two-cardinals Transfer Property and Resurrection of Supercompactness

We show that the transfer property (א1,א0)→ (λ+, λ) for singular λ does not imply (even) the existence of a non-reflecting stationary subset of λ+. The result assumes the consistency of ZFC with the existence of infinitely many supercompact cardinals. We employ a technique of “resurrection of supercompactness”. Our forcing extension destroys the supercompactness of some cardinals; to show that ...