Title: Computing the Number of Types of Infinite Length, Part 1.
Abstract: Roughly, the type of an element over a given domain is the best description of the element possible using formulas from the language and parameters from the domain. Counting the largest number of types of finite tuples possible over a domain of fixed size give important information about the theory and characterizes its place in relation to certain dividing lines, such as stability. It is known that it is enough to check stability just for 1-types. We generalize this result to types of infinite tuples of elements by calculating supremum number of types of infinite tuples over a domain of fixed size from the number of 1-types. In particular, for $\kappa \leq \alpha$, we show
Time: 5:00 pm
Location: Wean 8220