Projects

Reverse Mathematics (RM) unveils the striking phenomenon that theorems of ordinary Mathematics fall in only five equivalence classes, although there are infinitely many nonequivalent classes in Logic. My project analyzes RM where equality = is replaced with $\approx$, equality up to infinitesimals from Nonstandard Analysis. There are applications in Physics and the Philosophy of Science.

This project concerns an investigation into three aspects of the relation between mathematics and adaptive logics (AL's): it is investigated how (a) AL's can be used for the formal modeling of the mathematical practice, (b) AL's can solve problems of the foundations of mathematics, and © mathematical techniques can be used for the abstract study of AL's.

As all other sciences rely on mathematics, I think of science as a building, with the ground floor being made up by mathematics. As we want to keep the building in good shape so it can grow in a creative, new and strong way, we need to take care of the foundations. Logic represents these foundations. It provides the framework for mathematics (consisting of the assumptions we work with) and general abstract tools for considering mathematical ...

By work of Austrian logician Kurt Gödel in the 1930s, no sound and
sufficiently strong computably enumerable arithmetic theory can
prove its own consistency. Soon after Gödel's work, G. Gentzen
provided an almost finitary proof of the consistency of Peano
Arithmetic, with only one extraneous component: a use of transfinite
induction up to a suitable ordinal number.
Ordinal analysis is the branch of proof theory ...

The aim of this project is to develop, implement and apply several generation algorithms for combinational structures that are especially interesting in mathematics and chemistry. Furthermore we will extend the software package Grinvin and will continue our support for the applications of this package in teaching at high school and university level.