“Graph Theory and the Transfinite”
Martedì 1 Ottobre 2019, ore 16:30 - Aula 2AB45 - Michael Rathjen (University of Leeds, UK)
A bit more than a 100 years ago, as a response to the foundational crisis in mathematics, Hermann Weyl published his “Das Kontinuum” in which he tried to rebuild mathematics from a stance that assumes the existence of the set of natural numbers as an actual completed infinity but no higher infinities. Much later in the 1970s, logicians began to systematically scour various chunks of ordinary mathematics to determine the existential commitments to the infinite that they required. This is known as “Reverse Mathematics”. To put it roughly, it turned out that most of “ordinary” mathematics didn’t need more than what Weyl had assumed. However, there are some notable exceptions. In particular graph theory sports some very nice theorems that require more of the transfinite. The talk will discuss some famous theorems and their relationships with the infinite world.