Mathematical Logic: Proof Theory, Constructive Mathematics

Abstract

The workshop “Mathematical Logic: Proof Theory, Constructive Mathematics” brought together a carefully selected group of mathematicians, computer scientists and logicians in other fields to discus the impact of proof-theoretic and constructive methods in their various areas. A key topic in the meeting was the unwinding of proofs to obtain computational information. This hidden computational information has already lead to new mathematical insights. Computational information is more directly present in constructive approaches to mathematics, a fact that makes it worthwhile to carefully investigate these approaches and also study their proof-theoretic properties. The precise quantitative information proof theory yields about proofs and proof transformations can directly be applied to computational complexity.