Current trends in set theory

Abstract: Not all questions in mathematics can be answered in ZFC by Gödel's incompleteness theorems. Numerous concrete examples of mathematical statements have been proven to be independent from the ZFC axioms over the years. Many of them being non-set-theoretic in nature. Most notably, the Whitehead problem, the Borel conjecture, Kaplansky's conjecture on Banach algebras, or the Brown-Douglas-Fillmore problem. Instead of accepting that there are questions that don't have an answer, the independence phenomenon lead set theorists to search for axioms beyond ZFC that would give us a clearer picture of the set theoretic (and mathematical) universe.

In this talk I will present the main lineages of axioms that have been considered and their consequences. I will describe their connections and the main methods to study them, and I will finish by connecting all of this with my PhD thesis.

Mathematics

Audience: researchers in the topic

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.