Categories turned models: taming the finite

CUNY Logic WorkshopFriday, October 30, 20152:00 pmGC 6417

Hans Schoutens

Categories turned models: taming the finite

The City University of New York

Whereas a category theorist sees mathematics as objects interacting with each other via maps, a model theorist looks instead at their internal structure. So we may think of the former as the sociologues of mathematics and the latter as their psychologues. It is well-known that to a first-order theory we can associate the category of its models, but this produces often a non-natural category, as the maps need to be elementary, and maps rarely are! I will discuss the opposite (Jungian?) perspective: viewing a category as a first-order structure. This yields some unexpected rewards: it allows us to define certain second-order concepts, like finiteness, in a first-order way. I will illustrate this with some examples: sets, modules, topologies, …

Professor Schoutens is a professor of mathematics at the City University of New York, and conducts research in algebraic model theory, commutative algebra, algebraic geometry, rigid analytic geometry and valuation theory.

Posted by on October 15th, 2015