04-00-0166-vu Applied Proof Theory

Instructors: Prof. Dr. phil. nat. Ulrich Kohlenbach; Dr. Pedro Pinto

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: - | -

Digital Teaching:
The lectures are given live online via Zoom. Zoom meeting 819 8820 6495, PIN: 386304.
Recordings of these live lectures will subsequently be made available as well.

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:
"Introduction to Mathematical Logic" or "Aussagenlogik und Prädikatenlogik"

Expected Number of Participants:
20