Abstract
Mathematicians imagine a myriad of objects, most of them infinite, and
inevitably followed by an infinite suite. One way to understand them
consists of arranging them, ordering them. This act of organising
objects amounts to considering an instance of the very general
mathematical notion of a quasi-order. Well-founded quasi-orders play a
crucial role in many areas of mathematics, and so do the stronger
notions of well-quasi-orders and better-quasi-orders.
This first talk will be an introduction to better-quasi-orders. We will see that their definition hinges on a particularly interesting Borel graph: the shift graph. Its chromatic number is 2, but its Borel chromatic number is infinite.