Set theory seminarFriday, March 7, 201410:00 amGC6417

# The consistency strength of PFA for posets preserving aleph_2 or aleph_3

## Miha Habič

### The CUNY Graduate Center

While the consistency strength of PFA is quite high in the large cardinal hierarchy, it is reasonable to expect that tame fragments of PFA should require much weaker assumptions. I will present an argument of Hamkins and Johnstone (2008) which shows the consistency of PFA for posets preserving aleph_2 or aleph_3 from a strongly unfoldable cardinal, a much smaller large cardinal which is, roughly speaking, to strongness (or supercompactness) as weak compactness is to measurability.

This talk will serve as the speaker's Second Examination for his degree requirements in the Mathematics Ph.D. program of the CUNY Graduate Center.

Miha Habič is a graduate student at the CUNY GC. He got his Masters Degree in Mathematics at the University of Ljubljana, Slovenia. His interests lie in the area of infinitary computability, forcing and large cardinals.

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on February 28th, 2014