Brian Pinsky, Rutgers University

Abstract

The axiom of choice says "every set of non-empty sets has a choice function".  This has some well known, slightly problematic consequences.  However, abandoning AC can result in much much worse consequences (e.g. the reals are a countable union of countable sets).  This has led mathematicians think of lots of weaker axioms over the year.

In this talk, I'll give an overview of a bunch of several of these axioms.  Some are stronger than others, but which ones are how strong can be hard to tell.  The axioms "every set of n-element sets have a choice function" turn out particularly interesting; studying the implications will take us through some vary fancy combinatorics, and a presumably open question that's been bothering me for like years now.

This seminar is being held in person in The Hill Center,
Mathematics Graduate Student Lounge - 7th Floor
and online via a simultaneous broadcast on Zoom.
Zoom Link: https://rutgers.zoom.us/j/95142025758

Password: 557818

For further information see: https://sites.math.rutgers.edu/~ctk47/GCS.html