Special Colloquium
Dima Sinapova
University of California at Irvine
The singular cardinal problem
Abstract: Cardinal arithmetic has a long history, dating back to Cantor. After the
invention of forcing, any reasonable behavior of regular cardinals was shown
to be consistent. In contrast, results about singular cardinals are much
more intricate and require more than the standard axioms of set theory. I
will discuss relative consistency results about singular cardinal arithmetic
in the context of forcing and large cardinals. I will focus on the
relationship between the Singular Cardinal Hypothesis, which is a parallel of the
Continuum Hypothesis for singular cardinals, and combinatorial principles
such as Jensen's square principle, scales, and the tree property. I will
describe some recent consistency results about singular combinatorics and new
constructions involving Prikry type forcings.
Monday January 30, 2012 at 3:00 PM in SEO 636