## Past Seminars- Logic Set Theory

• Isaac Goldbring
Mon Jun 4, 2018
4:00 pm
In this continuation of my talk from last week, I will introduce the notion of a spectral gap subalgebra of a tracial von Neumann algebra and show how it connects to the definability of relative commutants.  I will also mention some applications of these results.  I will introduce all notions needed from the theory of von Neumann...
• Mauro Di Nasso
Wed May 30, 2018
4:00 pm
In  Ramsey  Theory, ultrafilters often play an instrumental role. By using nonstandard models of the integers, one can replace those third-order objects (ultrafilters are families of subsets) by simple points. In this talk we present a nonstandard technique that is grounded on the above observation, and show its use in proving some new...
• Sherwood Hachtman
Mon May 21, 2018
4:00 pm
Tree properties are a family of combinatorial principles that characterize large cardinal properties for inaccessibles, but can consistently hold for "small" (successor) cardinals such as $\aleph_2$.  It is a classic theorem of Magidor and Shelah that if $\kappa$ is the singular limit of supercompact cardinals, then $\kappa^+$ has...
• Isaac Goldbring
Mon May 14, 2018
4:00 pm
In this first of two talks, I will explain the notion of definability in continuous logic and connect it with the notion of spectral gap in the theory of unitary representations and in ergodic theory.
• Douglas Ulrich
Mon May 7, 2018
4:00 pm
How complicated are countable torsion-free abelian groups? In particular, are they as complicated as countable graphs? In recent joint work with Shelah, we show it is consistent with ZFC that countable torsion-free abelian groups are $a \Delta^1_2$ complete; in other words, countable graphs can be encoded into them ...
• Martin Ziegler
Mon Apr 30, 2018
4:00 pm
(This is joint work with Martin Pizarro). We prove that for any prime p the theory of separably closed fields of characteristic p is equational. This was known before for finite degree of imperfection.
• Ryan Sullivant
Mon Mar 12, 2018
4:00 pm
In this talk we develop iterability theory for a single measure, give an inner model theoretic representation of 0-sharp, and show how this representation leads to non-trivial embedding of L into L.