## 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

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)