Rethinking Reverse Mathematics: An Alternative Perspective 🧠

Speaker: Dag Normann, Professor emeritus at the University of Oslo

Nordic Logic Seminar: Monday, June 21, 16.00-17.30 CEST

Title: An alternative perspective on Reverse Mathematics

Abstract: In his address to the International Congress of Mathematics in Vancouver, 1974, Harvey Friedman launched a program where the aim would be to find the minimal set of axioms needed to prove theorems of ordinary mathematics. More than often, it turned out that the axioms then would be provable from the theorems, and the subject was named Reverse Mathematics.

In this talk I will survey some of the philosophy behind, and results of, the early reverse mathematics, based on the formalisation of mathematics within second order number theory.

In 2005, Ulrich Kohlenbach introduced higher order reverse mathematics, and I will give a brief explanation of the what and why? of Kohlenbach’s approach.

In an ongoing project with Sam Sanders we have studied the strength of classical theorems of late 19th/early 20th century mathematics, partly within Kohlenbach’s formal typed theory and partly by their, in a generalised sense, constructive content. In the final part of the talk I will give some examples of results from this project, mainly from the perspective of higher order computability theory. No prior knowledge of higher order computability theory is needed.