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Instructors: Prof. Dr. phil. nat. Ulrich Kohlenbach
Event type:
Lecture & Exercise
Org-unit: Dept. 04 - Mathematics
Displayed in timetable as:
Appl Proof Theory
Subject:
Crediting for:
Hours per week:
6
Language of instruction:
Englisch
Min. | Max. participants:
- | -
Course Contents:
This course develops the major techniques of applied proof theory, namely so-called proof interpretations together with applications to various areas of mathematics such as approximation theory, nonlinear analysis and ergodic theory. These applications are concerned with the extraction of effective bounds and new qualitative uniformity results from prima facie ineffective proofs. The main techniques studied are: Herbrand theory, no-counterexample interpretation (Kreisel), modified realizability (Kreisel), Gödel’s functional (‘Dialectica’) interpretation, negative translation (Gödel), functional interpretation of full analysis (Spector), monotone interpretations and their extensions to systems based on classes of abstract (nonseparable) metric, hyperbolic and normed spaces
Literature:
Kohlenbach, U.: Applied Proof Theory: Proof Interpretations and Their Use in Mathematics. Springer Monograph in Mathematics, xx+536pp., 2008
Preconditions:
recommended: Introduction to Mathematical Logic, Introduction to Computability Theory (useful)
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