Nonstandard methods versus Nash-Williams

This is a talk at the MAMLS Spring Fling 2023 conference on 23 May 2023.

[slides]

Combinatorics has long enjoyed being a site of application for nonstandard methods, using objects from ultrafilters to hyperintegers. In this talk I will discuss work from a joint project with Timothy Trujillo. We have been looking at applying nonstandard methods to the Nash–Williams partition theorem—an analogue of the infinite Ramsey theorem for certain families of finite sets of integers—and its generalizations to a broader class of Ramsey spaces.