Michaelmas Term 2020
Model Theory (Part III)Gabriel Conant, Research Associate
Time: MWF 12:00 (Cambridge)
Dates: Friday 9 October through Wednesday 2 December (24 lectures)
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
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
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.
- 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.
Please note that recordings of lectures and examples classes are only available to Cambridge students enrolled in the course Moodle.
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
- Lecture 0 (9 October)
review notes on first order logic - Lecture 1 (12 October)
review notes on compactness - Lecture 2 (14 October)
- Lecture 3 (16 October)
addendum to Definition 3.7 - Lecture 4 (19 October)
- Lecture 5 (21 October)
- Lecture 6 (23 October)
- Lecture 7 (26 October)
- Lecture 8 (28 October)
- Lecture 9 (30 October)
- Lecture 10 (2 November)
- Lecture 11 (4 November)
- Lecture 12 (6 November)
supplemental notes - Lecture 13 (9 November)
- Lecture 14 (11 November)
- Lecture 15 (13 November)
clarification on Corollary 15.4 - Lecture 16 (16 November)
correction to Example 16.5 - Lecture 17 (18 November)
- Lecture 18 (20 November)
- Lecture 19 (23 November)
- Lecture 20 (25 November)
- Lecture 21 (27 November)
- Lecture 22 (30 November)
supplemental notes - Lecture 23 (2 December)
- Examples Sheet 1 and notes from class
- Examples Sheet 2 and notes from class
- Examples Sheet 3 and notes from class
- Examples Sheet 4 and notes from class