Math 512 Advanced Topics in Logic

Model Theory and Infinitary Logic

Fall 2013

Course Meeting: 9:00 MWF 310 AH
Call Number: 344413
Instructor: David Marker
Office: 411 SEO
Office Hours: TBA
phone: (312) 996-3069
course webpage:


This will be a course on the model theory of infinitary languages focusing on the model theory of L_{omega_1,omega}. The first part of the course will an introduction to the basics: back-and-forth systems, Scott's isomorphism theorem, Henkin arguments, omitting types, prime models, up-Lowenheim Skolem Theorems and Hanf number considerations.

One major advanced topic is using infinitary methods to shed light on Vaught's Conjecture.

We will also look at issues about stability, existence of uncountable models, and categoricity questions. One goal will be to integrate recent work of Zilber, Baldwin, Larson, Laskowski, Koerwein and Friedman.

If time permits we may talk briefly about admissible sets and Barwise compactness.

There will be no homework.


The ideal preparation would include one semester each of model theory, descriptive set theory and set theory, but most of the material will be accessible to anyone with a modest understanding of graduate logic.


Comments: Keisler's book is sadly out of print. A copy should be on reserve at the library. The Barwise and Barwise-Feferman books are available electronically through the library. The article in Barwise-Feferman by Nadel is of particular interest. Baldwin's book is easily available.

Lecture Notes

The following are first drafts of the lecture notes. Beware of typos and small gaffs.