Blog Archives

Topic Archive: Forcing and Large Cardinals

Set theory seminarFriday, April 24, 20152:00 pmGC 6417

Erin Carmody

Dissertation Defense: Force to change large cardinals

The CUNY Graduate Center

This will be the dissertation defense of the speaker.  There will be a one-hour presentation, followed by questions posed by the dissertation committee, and afterwards including some questions posed by the general audience. The dissertation committee consists of Joel David Hamkins (supervisor), Gunter Fuchs, Arthur Apter, Roman Kossak and Philipp Rothmaler.

Set theory seminarFriday, May 16, 201410:00 amGC6417

Alexander Rapp

The Laver Preparation

The CUNY Graduate Center

I will present the result of Laver demonstrating that the existence of a supercompact cardinal implies the existence of a Laver function, and using this to construct a model with a supercompact cardinal k which remains supercompact in any k-directed-closed forcing extension.

Set theory seminarFriday, January 31, 201410:00 amGC 6417

Joel David Hamkins

Large cardinals need not be large in HOD

The City University of New York

I will demonstrate that a large cardinal need not exhibit its large cardinal nature in HOD. I shall begin with the example of a measurable cardinal that is not measurable in HOD, and then afterward describe how to force more extreme examples, such as a model with a supercompact cardinal, which is not weakly compact in HOD. This is very recent joint work with Cheng Yong.