21-803 Model Theory III
Rami Grossberg (Rami@cmu.edu)
URL: www.math.cmu.edu/~rami
MWF 3:30-4:20PM, WeH 8201
Starting date: Monday, January , 2020
12 Units

This will be different than courses I offered in the last two years. It will not depend on Model theory II offered in spring 2019.

I will concentrate in classification theory for first-order theories. The theory was developed mostly by Saharon Shelah presented in his 1978 (2nd ed 1990) book and in several hundreds of papers. I will present a modern overview of Shelah's theory incorporating few recent innovations and simplifications. The development of the theory was motivated by set-theoretic questions like: "what is the asymptotic behavior of the function I(\aleph_\alpha,T) as a function of \alpha ?" and "what is the first \lambda such that an uncountable first-order stable theory T is stable in \lambda?"

Surprisingly the full answer to such combinatorial set-theoretic questions led for a development and discovery of a conceptually rich theory which seems to be related to aspects of commutative algebra and algebraic-geometry. This theory found several applications in the form of solving fundamental problems in classical fields of mathematics among them geometry and number theory.

The focus will be on the simplest and most fundamental aspects of the pure theory. Primarily around a notion called forking and various characterizations of classes of theories.

The American Mathematical Society awarded in 2013 its "Steel prize for Seminal Contribution to Research" to Shelah for his 1990 book. [the prize is given out to logicians once in 10 years, the 2003 prize was shared by Jensen & Morley]
Among the reasons given: ... made model theory into a mature field, completely transforming its aims, methods, and ability to connect to algebra and geometry."

Prerequisites: Elementary model theory (21-603) or permission of the instructor. The pace of presentation will be faster than in 21-603.

Text: Rami Grossberg, A course in model theory I: An introduction, a book in preperation.
Table of contents (as of August 2019). This is the first volume in a three volume book series to be published by Cambridge University Press. The full text is available to registered students from a protected directory here. If you use this link, you agree not to publish it and not to share the contents.

Some of the material appears in the following books:

Accommodations for Students with Disabilities:
If you have a disability and are registered with the Office of Disability Resources, I encourage you to use their online system to notify me of your accommodations and discuss your needs with me as early in the semester as possible. I will work with you to ensure that accommodations are provided as appropriate. If you suspect that you may have a disability and would benefit from accommodations but are not yet registered with the Office of Disability Resources, I encourage you to contact them at access@andrew.cmu.edu.

Statement of Support for Students’ Health and Well-being
Take care of yourself. Do your best to maintain a healthy lifestyle this semester by eating well, exercising, avoiding drugs and alcohol, getting enough sleep and taking some time to relax. This will help you achieve your goals and cope with stress.
If you or anyone you know experiences any academic stress, difficult life events, or feelings like anxiety or depression, we strongly encourage you to seek support. Counseling and Psychological Services (CaPS) is here to help: call 412-268-2922 and visit http://www.cmu.edu/counseling/. Consider reaching out to a friend, faculty or family member you trust for help getting connected to the support that can help.
If you or someone you know is feeling suicidal or in danger of self-harm, call someone immediately, day or night:
CaPS: 412-268-2922 Re:solve Crisis Network: 888-796-8226 If the situation is life threatening, call the police On campus: CMU Police: 412-268-2323 Off campus: 911

If you have questions about this or your coursework, please let me know. Thank you, and have a great semester.

Rami's home page.
Last modified: January 15 nd, 2020