Lecture Course on Proof Theory

Graduate Course, January 31 - May 18, 2000


Anton Setzer,
Uppsala University, Dept. of Mathematics, Polacksbacken, House 2, Room 138.
Tel.: (018) 471-3284 (office), (018) 301348 (home)
email: Replace '_dot_' by '.' and '_at_' by '@' in 'a_dot_g_dot_setzer_at_swan_dot_ac_dot_uk'


The topic of proof theory is the study of axiom systems, in which mathematical proofs can be formalized, mainly subsystems of set theory and analysis. The main goal of a proof theoretic analysis is the determination of the proof theoretic ordinal of a theory, a measure for its strength. In order to determine it, the full power of an axiom system has to be used, much more than usual in mathematics, and a deep insight into these systems is obtained. Proof theoretic methods are often the only way to reduce impredicative systems to more constructive principles. Such reductions are useful for theoretical computer science, because they allow to obtain the computable content of proofs, and provide at the same time solid foundations for mathematics.

As part of the year on mathematical logic at the Institut Mittag Leffler, a research institute for mathematics located close to Stockholm, the best proof theoretists in the world will visit this place in spring 2001 for longer periods. This course is intended as well to be a preparation for these visits.



Logik MN1. Experience with logic in the form of one advanced logic course.


[Po89] Wolfgang Pohlers: Proof theory. Springer Lecture Notes in Mathematics 1407, 1989.
Research Articles

Further literature

[Sch77] Kurt Schütte: Proof theory. Springer, 1977.
[Gi87] Jean-Yves Girard: Proof theory and logical complexity, Vol. 1. Bibliopolis, Naples, 1987. (Available via Elsevier).
[Ta75] G. Takeuti: Proof theory. North-Holland, Amsterdam, 1975.


Uppsala University, Department of Mathematics, Polacksbacken, house 2.
(For those living in Stockholm: Train service Stockholm - Uppsala now twice per hour).


January 31 - May 18, 2000.


Monday 31.i.10-122345
Tuesday 1.ii.15-172114
No lecture on Thursday, 3.ii.
Monday 7.ii.15-172215
Tuesday 8.ii.10-122314
Thursday 10.ii.10-121146
Monday 14.ii.15-172215
Tuesday 15.ii.10-122314
Thursday 17.ii.10-121146
Monday 21.ii. - 10.iv.15-172214
Tuesdayfrom 22.ii. 10-122314
Thursdayfrom 24.ii.10-122314