Kurt Gödel Research Center

2009 seminar talk: The Resurrection Axioms

Talk held by Thomas Johnstone (KGRC and City Tech, New York) at the KGRC seminar on 2009-10-15.

Abstract

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 plan to illustrate how RA is tied to forcing axioms such as MA and BPFA, and how it affects the size of the continuum. The main theorem will show that RA and many instances of wRA are equiconsistent with the existence of an uplifting cardinal, a large cardinal notion consistent with V=L. This is joint work with Joel Hamkins.