Welcome to the webpage of the logic group at the University of Gothenburg. Information about our research and activities can be found through the links to the left. More detailed information is available through the personal pages of group members and our homepage at the University of Gothenburg.
In its modern formulation, Hilbert’s tenth problem asks to find a general algorithm which decides the solvability of Diophantine equations. While this problem was shown to be unsolvable due to the combined work of Davis, Putnam, Robinson and Matiyasevich, similar question can be posed over domains other than the integers. Among the most important open questions in this area of research is if a version of Hilbert’s tenth problem for Fp((t)), the field of formal Laurent series over the finite field Fp, is solvable or not.
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 we 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.