# Riccardo Bruni

- July 2016

###### Set existence and choice principle: Beppo Levi’s contribution to foundations of mathematics

Beppo Levi is best known for his work in analysis, number theory, measure theory and set theory. His contribution to metamathematical and foundational issues is less known instead. The aim of this talk is to present it by focusing on two topics: Levi’s peculiar approach to set theory and set existence, and his proposal of a principle alternative to the axiom of choice. In both cases we try to recast Levi’s ideas in modern terms and discuss their mathematical and philosophical significance.