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.
Lehrinhalte
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), Gödels 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
Voraussetzungen
"Introduction to Mathematical Logic" or "Aussagenlogik und Prädikatenlogik"
Erwartete Teilnehmerzahl
20
Bemerkung Webportal
im Wechsel mit anderen Lehrveranstaltungen des Forschungsgebietes Logik
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.
Lehrinhalte
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), Gödels 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
Voraussetzungen
"Introduction to Mathematical Logic" or "Aussagenlogik und Prädikatenlogik"
Erwartete Teilnehmerzahl
20
Bemerkung Webportal
im Wechsel mit anderen Lehrveranstaltungen des Forschungsgebietes Logik
- Lehrende: Ulrich Kohlenbach
- Lehrende: Pedro Pinto
Semester: Verão 2021