Description
This course is an introduction to first-order model theory. We will cover a selection of topics, such as complete theories and elementary equivalence, categoricity, quantifier elimination, type spaces, atomic and saturated models, the Omitting Types Theorem, and an introduction to stability theory.
Logistics
- Zoom: All lectures, examples classes, and weekly office hours will be delivered remotely via Zoom using the same recurring meeting. The meeting ID, passcode, and a direct link are available in the course Moodle.
- Lectures: I will give live lectures using a note-writing app (shared screen). Video recordings and lecture notes will be made available in the course Moodle. The lecture notes have also been posted below.
- Examples classes: There will be four examples classes (schedule TBA). These sessions will also be recorded and posted to the course Moodle. A problem set will be made available in advance of each class, and a selection of problems will be assigned for marking.
Please note that recordings of lectures and examples classes are only available to Cambridge students enrolled in the course Moodle.
- Office Hours: I will be available on Mondays 3:30 - 4:30 for an extra office hour each week other than the weeks with examples classes. The first office hour will be on Monday 12 October.
- Appointments: I am happy to make additional Zoom appointments to discuss the course material and problem sets. Email me to schedule a time.
Prerequisites
The only prerequisite for the course is Logic and Set Theory (Part II) or equivalent. This includes basic concepts from first-order (predicate) logic such as languages, structures, satisfaction, and the Compactness Theorem. Familiarity with ordinals, transfinite induction, and basic point-set topology will also be helpful.
Resources
The course will loosely follow
Model Theory: An Introduction (by Dave Marker). I believe this book is available online from the Cambridge university library (via Proquest). Dave Marker's
MSRI notes are written in a similar style as the book.
Lecture Notes
Examples Class Notes
Exam Review