Abstract: I will give an overview of the basics of continuous first-order logic, emphasizing similarities and differences with discrete first-order logic. I will then discuss some current research directions.
Abstract: I will introduce the concept of definable sets in continuous logic, presenting visual examples of their sometimes strange behavior. I will then develop a tameness condition under which they are more manageable. This will lead into some open questions.
Abstract: We examine three products on classes of structures, the semi-direct product, the direct product, and the free superposition. We investigate what properties of classes of structures, such as indivisibility and age indivisibility, are preserved under each product. This work is joint with Miriam Parnes and Lynn Scow.
Abstract: We will present a new coherent framework based on the theory of transportation cost (Arens Eells) spaces for showing some new and old results connecting amenability of groups, topological dynamics and Ramsey theory of classes of finite structures.
This is part of a collaboration with Todor Tsankov.
Abstract: HALT is undecidable. But what if you could make 5 queries to HALT? Then what could you compute? Could you computer more than if you could only make 4? What about other undecidable sets? Come and find out!
Abstract: We define and discuss cellular, mutually algebraic, monadically NIP and monadically stable theories and see how they interrelate in terms of (worst case) expansions by unary predicates. Many results will be stated, but also a few open problems will be presented. Much of the newer work is joint with Sam Braunfeld.
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