Math 255 Classification Theory for Tame Abstract Elementary Classes

Starting from the definition of Abstract Elementary Classes (AECs), we will develop nonforking and classification theory for tame AECs. These classes are general enough to encompass interesting examples of nonelementary classes, but have enough structure to develop a reasonable classification theory. We will cover the construction of good frames and other nonforking notions in tame AECs; examples of tame AECs; and the impact of set theory and large cardinals.

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Lecture Notes

Lecture notes (Updated 9/14)


The best textbook for learning about Abstract Elementary Classes is John Baldwin's Categoricity (with errata). Other good survey's include Rami Grossberg's "Bilgi" paper (actually titled Classification Theory for Abstract Elementary Classes) and Sebastien Vasey and my recent A Survey on Tame Abstract Elementary Classes (which is a survey on tame Abstract Elementary Classes). This list wouldn't be complete without Saharon Shelah's two-volume Classification Theory for Abstract Elementary Classes. This is substantially more advanced than the other references. While not formally available online, it's chapters (mostly) consist of previously unpublished papers or substantial revisions of papers which are individually available on Shelah's website. For instance, the very accessible introduction is [ShE53].

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