NIP theories and Shelah's Theorem

Abstract

These are the (informal and expanded) notes of a mini-course given in the Universidad Autónoma de Madrid, 29-30 of May 2018 (6 hours). The mini-course was given at the end of a master course on Model Theory with applications to Algebra. The purpose of the mini-course is to introduce the students to modern pure model theoretic tools. Specifically, our purpose is the give the definition of stable theory, to give the definition of NIP theory and to give the statement and some hints of the proof of Shelah’s Theorem (which says that if we add to the language the externally definable sets of a model of a NIP theory, then the theory remains NIP).