## Past Seminars- Logic Set Theory

• Sean Cox
Mon Jan 8, 2018
4:00 pm
Shelah proved that a certain form of Strong Chang’s Conjecture is equivalent to the  statement Namba forcing is semiproper". I will present some related results about semiproperness of nonreasonable” posets (a notion introduced by Foreman-Magidor). This is joint work with Hiroshi Sakai.
• Scott Cramer
Mon Dec 4, 2017
4:00 pm
We will investigate algebraic structures created by rank-into-rank elementary embeddings. Our starting point will be R. Laver's theorem that any rank-into-rank embedding generates a free left-distributive algebra on one generator. We will consider extensions of this and related results. Our results will lead to some surprisingly coherent...
• Toby Meadows
Mon Nov 27, 2017
4:00 pm
In this talk, I’ll sketch a way of unifying a wide variety of set theoretic approaches for generating new models from old models. The underlying methodology will draw from techniques in Sheaf Theory and the theory of Boolean Ultrapowers.
• Kino Zhao
Mon Nov 20, 2017
4:00 pm
One of the primary theoretical tools in machine learning is Vapnik-Chervonenkis dimension (VC dimension), which measures the maximum number of distinct data points a hypothesis set can distinguish. This concept is primarily used in assessing the effectiveness of training classification algorithms from data, and it is established that having finite...
• Aristotelis Panagiotopoulos
Mon Nov 13, 2017
4:00 pm
Classification problems occur in all areas of mathematics. Descriptive set theory provides methods to assign complexity to such problems. Using a technique developed by Hjorth, Kechris and Sofronidis proved, for example, that the problem of classifying all unitary operators $\mathcal{U}(\mathcal{H})$ of an infinite dimensional Hilbert space up to...
• Nick Ramsey
Mon Nov 6, 2017
4:00 pm
Simplicity theory, a core line of research in pure model theory, is built upon a tight connection between a combinatorial dividing line (not having the tree property) and a theory of independence (non-forking independence).  This notion of independence, which generalizes linear independence in vector spaces and algebraic independence in...
• Jeffrey Bergfalk
Mon Oct 16, 2017
4:00 pm
We describe a number of related questions at the interface of set theory and homology theory, centering on (1) the additivity of strong homology, and (2) the cohomology of the ordinals. In the first, the question is, at heart: To how general a category of topological spaces may classical homology theory be continuously extended? And in the tension...