The Scandinavian Logic Society

NOL Seminar with Dag Normann

The Nordic Online Logic Seminar is organised monthly over Zoom, with expository talks on topics of interest for the broader logic community. The seminar is open for professional or aspiring logicians and logic aficionados worldwide. If you wish to receive the Zoom ID and password for it, as well as further announcements, please subscribe here: https://listserv.gu.se/sympa/subscribe/nordiclogic.

Next talk: Monday, June 21, 16.00-17.30 CEST (UTC+2), on Zoom (details will be provided to the subscribers)

Title: An alternative perspective on Reverse Mathematics

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

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.