Digital Teaching
If current regulations allow it, I intend to deliver the course in person. In any case, it will also be possible to follow the course remotely.
It seems that [b]course registration opens on 20 September[/b] (rather than 1 September as usual; this has to do with additional planning requirements in connection with COVID-19). If you have questions before that date, please feel free to contact the lecturer.
Lehrinhalte
This course has a general and a specific goal: On a general level, the course is an introduction to ordinal analysis and some aspects of reverse mathematics, i.e., to two important areas of logic, with connections to proof theory, computabulity theory and combinatorics. As for the specific goal mentioned above, the course will give a complete proof of a famous result due to Harvey Friedman: Kruskal's theorem for binary trees (an important combinatorial result with applications in computer science) is unprovable in (conservative extensions of) Peano arithmetic. This offers a concrete mathematical example of the independence phenomenon from Gödel's theorems.
Literature
Detailed lecture notes will be available via Moodle. Additional reading is not required, but if you want to get a first impression, the following provides interesting background (see in particular Appendix E):
Michael Rathjen and Wilfried Sieg, "Proof Theory",
in Edward N. Zalta (ed.): The Stanford Encyclopedia of Philosophy (Fall 2020 Edition),
[url]https://plato.stanford.edu/archives/fall2020/entries/proof-theory/[/url]
Voraussetzungen
The canonical prerequisite is the course "Introduction to Mathematical Logic" (for Mathematicians) or the course "Aussagen- und Prädikatenlogik" (for Computer Scientists). If you are not sure whether you have the required prerequisites, please feel free to contact the lecturer.
Online-Angebote
It is crucial that you [b]register on Moodle[/b] as well as TUCaN. Most information and material (lecture notes, exercise sheets, etc.) will be published via Moodle. To contact the lecturer, it is better to write a message via Moodle than via TUCaN.
If current regulations allow it, I intend to deliver the course in person. In any case, it will also be possible to follow the course remotely.
It seems that [b]course registration opens on 20 September[/b] (rather than 1 September as usual; this has to do with additional planning requirements in connection with COVID-19). If you have questions before that date, please feel free to contact the lecturer.
Lehrinhalte
This course has a general and a specific goal: On a general level, the course is an introduction to ordinal analysis and some aspects of reverse mathematics, i.e., to two important areas of logic, with connections to proof theory, computabulity theory and combinatorics. As for the specific goal mentioned above, the course will give a complete proof of a famous result due to Harvey Friedman: Kruskal's theorem for binary trees (an important combinatorial result with applications in computer science) is unprovable in (conservative extensions of) Peano arithmetic. This offers a concrete mathematical example of the independence phenomenon from Gödel's theorems.
Literature
Detailed lecture notes will be available via Moodle. Additional reading is not required, but if you want to get a first impression, the following provides interesting background (see in particular Appendix E):
Michael Rathjen and Wilfried Sieg, "Proof Theory",
in Edward N. Zalta (ed.): The Stanford Encyclopedia of Philosophy (Fall 2020 Edition),
[url]https://plato.stanford.edu/archives/fall2020/entries/proof-theory/[/url]
Voraussetzungen
The canonical prerequisite is the course "Introduction to Mathematical Logic" (for Mathematicians) or the course "Aussagen- und Prädikatenlogik" (for Computer Scientists). If you are not sure whether you have the required prerequisites, please feel free to contact the lecturer.
Online-Angebote
It is crucial that you [b]register on Moodle[/b] as well as TUCaN. Most information and material (lecture notes, exercise sheets, etc.) will be published via Moodle. To contact the lecturer, it is better to write a message via Moodle than via TUCaN.
Semester: WT 2021/22