Math 269X Model theory for abstract elementary classes (Spring 2018)

Instructor: Sebastien Vasey
Office: Science Center 321H
Email: sebv (at) math (dot) harvard (dot) edu
Office hours: By appointment
Lectures: MWF 11AM-12PM SC 310

News / Announcements

• April 17, 2018: A new version of the lecture notes is online (except for typo fixes, no more updates will be made)!
• April 11, 2018: A new version of the lecture notes is online!
• April 6, 2018: A new version of the lecture notes is online!
• April 3, 2018: A new version of the lecture notes is online!
• March 27, 2018: A new version of the lecture notes is online!
• March 20, 2018: A new version of the lecture notes is online!
• March 6, 2018: A new version of the lecture notes is online!
• February 27, 2018: A new version of the lecture notes is online!
• February 13, 2018: A new version of the lecture notes is online!
• February 6, 2018: A new version of the lecture notes is online!
• January 30, 2018: A new version of the lecture notes is online!
• January 24, 2018: The first version of the lecture notes is up!
• January 11, 2018: This webpage is online, hurray! Please read the syllabus.

Lecture notes

Lecture notes (last updated April 26, 2018).

Other course documents

• Course syllabus.
• Tentative schedule (last updated Feb. 2, 2018; now out of date).

Other resources

Last Fall, Will Boney gave a course on abstract elementary classes which also had lecture notes. The focus of the present course will be different, and I will try not to repeat too many proofs that Will presented while staying self-contained. Will's notes may still be helpful.

Most chapters of Saharon Shelah's 2009 books are available online from the list of Shelah's papers.

• Volume 1:
  • Introduction: Sh:E48 Introduction to: classification theory for abstract elementary class.
  • Chapter 1: Sh:88r Abstract elementary classes near ℵ₁.
  • Chapter 2: Sh:600 Categoricity in abstract elementary classes: going up inductively.
  • Chapter 3: Sh:705 Toward classification theory of good λ frames and abstract elementary classes.
  • Chapter 4: Sh:734 Categoricity and solvability of A.E.C., quite highly.
• Volume 2:
• Chapter 1: A revised version of Sh:300: Universal classes, Classification theory (Chicago, IL, 1985) (1987) 264–418.
• Chapter 2: Sh:E46: Categoricity of an abstract elementary class in two successive cardinals, revisited (This is a revised version of Sh:576).
• Chapter 3: Sh:838: Non-structure in λ⁺⁺ using instances of WGCH.