
Proof Theory
Credits 
8 credit points 
Instructors 
Iemhoff, R. (Universiteit Utrecht), Oosten, J. van (Universiteit Utrecht) 
Email 
Rosalie.Iemhoff@phil.uu.nl, j.vanoosten@uu.nl 
Description 
Description: Proof Theory is the study of combinatorial properties of formal proofs in Logic. As such, the subject has relations with Combinatorics and Complexity Theory. The subject arose out of "Hilbert's Programme", an attempt to establish the consistency (that is: being free of contradictions) of ordinary mathematical reasoning, by finitary methods. First major results were obtained by Hilbert himself, Goedel, and Hilbert's assistants Paul Bernays and Gerhard Gentzen. In this course, we aim to acquaint the students with some basic results and techniques of the field. We shall start by working through the text "An Introduction to Proof Theory" by Samuel R. Buss. After that, there is a choice of additional topics we might discuss: Proof Complexity, Proof Theory of Arithmetic, Dialectica Interpretation and NoCounterexample Interpretation, Combinatorics of finite trees. 
Examination 
Written exam. 
Literature 
Literature: Required is Buss's text "An Introduction to Proof Theory"; available here. By the same author, there are the texts "Firstorder Proof Theory of Arithmetic" and "Propositional Proof Complexity, An Introduction". We might also make use of "A course in Proof Theory" by Herman Ruge Jervell.
Background Literature: we recommend Troelstra & Schwichtenberg, Basic Proof Theory (CUP, 2d edition1999), Girard, Proof Theory and Logical Complexity (Bibliopolis 1987) and Kohlenbach, Applied Proof Theory (Springer 2008). 
Prerequisites 
Prerequisites: bachelor in Mathematics. Familiarity with the basics of logic (language, structures, formal proofs) helps, but is not required. 
Remarks 
For more information, please visit this website. 
