Unprovability in Mathematics: A First Course on Ordinal Analysis
Logic
2022-04-22 v2
Abstract
These are the lecture notes of an introductory course on ordinal analysis. Our selection of topics is guided by the aim to give a complete and direct proof of a mathematical independence result: Kruskal's theorem for binary trees is unprovable in conservative extensions of Peano arithmetic (note that much stronger results of this type are due to Harvey Friedman). Concerning prerequisites, we assume a solid introduction to mathematical logic but no specialized knowledge of proof theory. The material in these notes is intended for 12 lectures and 6 exercise sessions of 90 minutes each.
Cite
@article{arxiv.2109.06258,
title = {Unprovability in Mathematics: A First Course on Ordinal Analysis},
author = {Anton Freund},
journal= {arXiv preprint arXiv:2109.06258},
year = {2022}
}