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Model Theory Seminar
Marcos Mazari Armida Carnegie Mellon University Title: Introduction to good frames in Abstract Elementary Classes, Part 1 Abstract: The central notion of Shelah's book on Abstract Elementary Classes [Sh:h] is the notion of a good $\lambda$-frame. It is a forking like notion for types over models of size $\lambda$ and the existence of it implies that the class is well-behaved in $\lambda$. In this series of talks we will focus on the question of the existence of extensions to models of size greater than $\lambda$. We will prove that under some reasonable hypothesis it is always possible to extend a frame. One interesting corollary of this is the existence of arbitrary large models, this is done within ZFC. The first couple of lectures will be based on [Sh:h] Chapter II, while our main theorem is the main theorem of [Bon14a]. References:[Bon14a] Will Boney, Tameness and extending frames, Journal of Mathematical Logic 14, no. 2[Sh:h] Saharon Shelah, Classication Theory for Abstract Elementary Classes, vol. 1 & 2, Mathematical Logic and Foundations, no. 18 & 20, College Publications, 2009. Date: Monday, September 18, 2017 Time: 5:00 pm Location: Wean Hall 8201 Submitted by: Grossberg |