When is a set of reals "weird"?

Abstract: The axiom of choice guarantees the existence of "weird" or "pathological" sets of real numbers and their relatives. Examples include well orderings of the reals, Lebesgue non-measurable sets and non-principle ultrafilters (which can be coded as a set of reals). The guiding framework here is that such sets cannot be "defined" in the sense that they have no explicit definition, which is why they do not come up so often in analysis and related fields. In this talk I will try to explain what this means more precisely as well as show that, in some models of set theory, "weird" sets actually have rather nice definitions. Time permitting, I will sketch some recent joint work with Jeffrey Bergfalk and Vera Fischer showing that consistently many pathological sets of reals can have very simple definitions all at the same time.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theorycomplex variablesfunctional analysislogicmetric geometryoptimization and control

Audience: researchers in the topic

VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

Meetings will be conducted over Zoom:

Meeting ID: 951 0562 0974

The password is 10 characters, consisting of the name of the ancient Greek mathematician who wrote "Elements" (first letter capitalized) followed by the first 4 primes.