معلومات المساق

Course Contents
This course is a continuation of the course `Basic Applied Proof Theory' and corresponds taken together with the latter with the 4+2 hours course `Applied Proof Theory'. The course develops the Gödel functional interpretation of full analysis (Spector), monotone interpretations of analysis and their extensions to systems based on classes of abstract (nonseparable) metric, hyperbolic and normed spaces. In applications to concrete proofs in mathematics we apply these techniques to analyze proofs in the areas of approximation theory, metric fixed point theory and ergodic theory. These applications are concerned with the extraction of effective bounds and new qualitative uniformity results from prima facie ineffective proofs.

Literature
Kohlenbach, U.: Applied Proof Theory: Proof Interpretations and Their Use in Mathematics. Springer Monograph in Mathematics, xx+536pp., 2008

Preconditions
recommended: Basic Applied Proof Theory