Date: Thursday, September 21, 2017
Location: 3096 East Hall (4:00 PM to 5:30 PM)
Title: A Category Theoretic Perspective on Continuous Logic
Abstract: Although classical model theory is largely formulated in terms of the framework of sets, there is a rich theory that casts model theoretic structures in a category theoretic setting, a project which began with Lawvere's thesis on "functorial semantics of algebraic theories" and has since grown into an important subfield of category theory. This interface between classical model theory and category theory continues to be an active area of research today.
In parallel, Lawvere also showed that structures  such as metric spaces  seemingly unrelated to categories arose naturally as examples of categories with appropriate enrichments V (for example V=R in the case of metric spaces). Now continuous logic/metric model theory is a generalization of classical model theory that, roughly, replaces sets with metric spaces and equality with the metric; a natural question to ask is whether the above perspective on metric spaces combines with the way of interpreting classical logic into category theory to produce a way to interpret continuous logic into enriched category theory. This talk will answer this in the affirmative, under reasonable conditions. The talk will make every effort to be selfcontained, and as such will assume little to no prior knowledge of category theory
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Speaker: Simon Cho
Institution: University of Michigan
Event Organizer: David Fernandez Breton logiclist@umich.edu
