Abstract

Introduction to the research area Proof theory traditionally aims at completing Hilbert's program, as revised in the light of Godels incompleteness theorem. As a prerequisite of the progress made there are certain results concerning structural properties of proofs in basic mathematical theories. These results have more and more came to the front during the last few decades, since besides of their applications in Hilbert's program they are of considerable interest from a logical and mathematical point of view and have several applications in philosophy as well as in computer science. The project enter into this research on the structure of proofs. A certain normal form of a proof is taken as a central concept. The notion of a normal proof goes back to the works of the german mathematician Gerhard Gentzen and has been further developed by Swedish logicians, principally Per MartinL of and Dag Prawitz. A characteristic of a normal proof is the absence of certain detours in the pro

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