21-803 Model Theory III
12 units, Carnegie Mellon University
We will concentrate in classification theory for firstorder theories. The theory was developed mostly by Saharon Shelah presented in his 1978 2nd ed 1990 book and in several hundreds of papers. We will present a modern overview of Shelahs theory incorporating few recent innovations and simplifications. The development of the theory was motivated by settheoretic questions like what is the asymptotic behavior of the function Ialephalpha,T as a function of alpha and what is the first lambda such that an uncountable firstorder stable theory T is stable in lambda Surprisingly the full answer to such combinatorial settheoretic questions led for a development and discovery of a conceptually rich theory which seems to be related to aspects of commutative algebra and algebraicgeometry. 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. Three 50 minute lectures
Prerequisites: (21-355 (min B) or 21-235 (min B) or 21-455 (min B)) and (21-373 (min B) or 21-237 (min B)) and 21-703 (min B)
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