Introduction

Abstract

Proof theory is a technical sub-field of mathematical logic which originated during the intense discussions of the foundations of mathematics in the first half of this century. David Hilbert (1862–1943) and his co-workers created it, and the original main purpose of it was to secure once and for all the consistency of mathematics. This consistency proof should be based on such elementary methods that it would be transparent and evident to everybody from all sides of the mathematical “Grundlagenstreit”. If this succeeded the foundational crisis of mathematics would come to an end and mathematicians could confidently proceed with their creative activity.