Speaker: Krishan Canzius

Abstract: The compactness theorem tells us that an infinite set of axioms will lead to a contradiction if and only if some finite subset does. The name suggests a connection to topology: we will see that the theorem tells us that a certain topological space is compact. We will also cover some applications of the theorem to fields outside of logic. Along the way we’ll discuss strange, non-standard models of familiar theories as well as infinite structures that behave as though they are finite.