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."

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:

- J. Baldwin, Fundamentals of stability theory.
- S. Buechler, Essential Stability theory.
- A. Pillay, Stability.
- Bruno Poizat, A course in Model Theory, Springer-Verlag 2000.
- Saharon Shelah, Classification Theory North-Holland 1990. This is the most important and difficult book in model theory. A free copy is available from his web site .
- Katrin Tent and Martin Ziegler, A course in model theory.

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 Studentsâ€™ 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 |