Digital Teaching
Currently I assume that the lecture will take place in person. If there is demand, I will try to make digital participation possible as well.
Lehrinhalte
We study advanced topics of ordinal analysis, such as predicative cut elimination (with infinite formula ranks) and collapsing. These techniques allow to prove one of the most famous independence results: the unprovability of the graph minor theorem in a strong system of second order arithmetic (due to Friedman-Robertson-Seymour). In case you want to get a more detailed impression, you can read Sections 5.2 and 5.3 as well as Appendix E of the following paper (but this is not a prerequisite for participating in the lecture):
[url]https://plato.stanford.edu/entries/proof-theory/[/url]
Literature
The will be lecture notes, which include a list of further references.
Voraussetzungen
It is expected that participants are familiar with the content of the lecture "Unprovability in Mathematics" delivered in Winter Term 2021/22. There are notes for this lecture, which are publicly available:
[url]https://arxiv.org/abs/2109.06258[/url]
In principle, it is possible to learn the required prerequisites by studying these notes on your own, even though this will require some commitment.
Online-Angebote
It is crucial that you also register for the course on Moodle. Some information will only be available via Moodle, so that you should keep an eye on the Moodle page and possibly register for email notifications.
Currently I assume that the lecture will take place in person. If there is demand, I will try to make digital participation possible as well.
Lehrinhalte
We study advanced topics of ordinal analysis, such as predicative cut elimination (with infinite formula ranks) and collapsing. These techniques allow to prove one of the most famous independence results: the unprovability of the graph minor theorem in a strong system of second order arithmetic (due to Friedman-Robertson-Seymour). In case you want to get a more detailed impression, you can read Sections 5.2 and 5.3 as well as Appendix E of the following paper (but this is not a prerequisite for participating in the lecture):
[url]https://plato.stanford.edu/entries/proof-theory/[/url]
Literature
The will be lecture notes, which include a list of further references.
Voraussetzungen
It is expected that participants are familiar with the content of the lecture "Unprovability in Mathematics" delivered in Winter Term 2021/22. There are notes for this lecture, which are publicly available:
[url]https://arxiv.org/abs/2109.06258[/url]
In principle, it is possible to learn the required prerequisites by studying these notes on your own, even though this will require some commitment.
Online-Angebote
It is crucial that you also register for the course on Moodle. Some information will only be available via Moodle, so that you should keep an eye on the Moodle page and possibly register for email notifications.
Semester: ST 2022