See you in the fall...

Math 873 - Fall 2016 - Topics in Logic - Continuous Model Theory and Applications

Instructor: Uri Andrews

Prerequisites: Math 776 optional

Time and Place: MWF 12:05 - 12:55

Textbook: none

Course Description: Recently, model theory has become a rich area of research with many interactions to other fields: algebra, combinatorics, number theory, etc. Yet until recently, the inherrently discrete nature of model-theoretic analysis prevented model theory from offering these same tools to more continuous structures. Thus enters continuous model theory. In continuous model theory, rather than having a Boolean truth value (true or false), every statement can be given a truth value in a bounded interval in the reals (say, like a probability of an event in a probability space or a distance in a metric space).

In the first part of the semester, we will develop the general theory of continuous model theory. Though much is done analogously to standard first-order logic, our development will (necessarily) be from the foundation, and thus this course can be taken without having taking Math 776.

In the latter part of the semester, we will look at particular theories and discuss applications of continuous model theory to the study of Hilbert spaces, probability algebras, Banach lattices, ergodic theory, Keisler randomizations, the Urysohn sphere, and perhaps others. Given time, we will also touch on some recent work in the theory of operator algebras from the perspective of continuous logic.

Math 975 - Reading Seminar in Logic

Our reading seminar is meeting on Wednesdays at 3:30.

Abstracts of talks

Makuluni's talk: Mirroring in convex orderings

We consider convexly orderable (CO) structures, i.e., those in which the definable sets in the home sort are uniformly finite unions of convex sets in some (possibly not definable) order. We look specifically at ordered CO structures and consider how the convex order relates to the ordering the structure was already equipped with. In particular, we show that discretely ordered convexly orderable structures satisfy a periodicity condition on definable sets and deduce that these structres have discrete convex orderings.


Prepared by Steffen Lempp (@math.wisc.edu">lemppmath.wisc.edu)