RUMA Seminar: Michael Fiore — Mapping the Universe: Models, Stability, and Independence

Classical model theory studies the relationship between statements written in first-order logic and set-theoretic structures which interpret them. Beginning primarily with the work of Shelah, much of work in the field became dedicated to the herculean task of classifying all first-order theories according to their behavior, categorized in meaningful ways by certain "dividing lines." We will introduce two characterizations of "good behavior" in first-order theories: stability and NIP, and present a two-cardinal theorem of Lachlan and Shelah that demonstrates what can be achieved within stable theories.