# Blog Archives

# Topic Archive: nearly supercompact

Set theory seminarFriday, September 14, 201210:00 amGC 6417

# The least weakly compact cardinal can be unfoldable, weakly measurable and nearly theta-supercompact

The City University of New York

Starting from suitable large cardinal hypothesis, I will explain how to force the least weakly compact cardinal to be unfoldable, weakly measurable and, indeed, nearly θ-supercompact. These results, proved in joint work with Jason Schanker, Moti Gitik and Brent Cody, exhibit an identity-crises phenomenon for weak compactness, similar to the phenomenon identified by Magidor for the case of strongly compact cardinals.