Logic Seminar

UCLA MS 6221

We show that the category of standard Borel spaces is the free or "universal" category equipped with some familiar set operations of countable arity (e.g., products) obeying some simple compatibility conditions (e.g., products distribute over disjoint unions). In this talk, we will discuss the precise formulation of this result, its connection with the amalgamation property for $\kappa$-complete Boolean algebras, and its proof using methods from categorical logic.