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Instructors: Prof. Dr. phil. nat. Ulrich Kohlenbach
Event type:
Lecture & Exercise
Org-unit: Dept. 04 - Mathematics
Displayed in timetable as:
04-10-0324-vu
Subject:
Crediting for:
Hours per week:
3
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Literature:
Ulrich Kohlenbach: Applied Proof Theory, Proof Interpretations and Their
Use in Mathematics. Springer Monograph in Mathematics. xix+536 Seiten,
2008.
Preconditions:
Introduction to Mathematical Logic
Basic Applied Proof Theory
Expected Number of Participants:
10
Official Course Description:
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.
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