Chris Lambie-Hanson: Well-orderings in logic and mathematics

Though not as glamorous as some of its relatives, the notion of well-ordering is arguably one of the most important and useful ideas in mathematical logic and set theory, lying at the heart of a number of important breakthroughs over the last 150 years. We will survey the valuable role that well-orderings and the Well-Ordering Theorem have played in the development of the modern foundations of mathematics and in applications of logic and set theory to other areas of mathematics. We will cover over 100 years of research, from the late 19th century to the present day, along the way investigating the roles that well-orderings play in connection with constructions of pathological mathematical objects, infinitary logics, questions of definability, large cardinals, and infinite games.