Infinite Exponent Ramsey Theory

John Howe, University of Leeds. Part of the postgraduate logic seminar series.

The starting point for my talk will be Ramsey's celebrated theorem that for any finite r, any finite colouring of r-sized subsets of the naturals has an infinite set from which all subsets are the same colour. I will then look at what happens when you consider infinite subsets rather than finite ones. This becomes substantially more complicated and draws in connections to descriptive set theory and various forms of the axiom of choice.

John Howe, University of Leeds