Steven Lazzaro, Department of Pure Mathematics, University of Waterloo
“Model theory learning seminar”
Given a complete theory, for types over a model, we will define three special extensions to supersets of the model, called heirs, coheirs, and definable extensions. At face value, these three types of extensions are quite different notions, although one key property they have in common is that any such extension does not add too much new information to the type, in a sense. In later discussions, we will see that these notions coincide in stable theories, and are furthermore unique given a fixed superset of the model. In this talk, we will introduce each of the three extensions and list some of their basic properties and interactions with each other.
MC 5417