## Past Seminars- Logic Set Theory

• Alec Fox
Mon Oct 22, 2018
4:00 pm
This is the third in a series of lectures on naive descriptive set theory based on an expository paper by Matt Foreman. We continue the discussion of universality properties of Polish spaces and subspaces of Polish spaces.
• Alec Fox
Mon Oct 15, 2018
4:00 pm
This is the second in a series of lectures on naive descriptive set theory based on an expository paper by Matt Foreman. The topics discussed will include tree representations, universality properties of Polish spaces, and subspaces of Polish spaces.
• Alec Fox
Mon Oct 8, 2018
4:00 pm
This is the first in a series of introductory lectures in descriptive set theory, following Matt Foreman's expository paper. The topics discussed will be basics of Polish topologies, product topologies, Cantor space and Baire space, and infinite trees.
• 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.