Impredicativity and Trees with Gap Condition: A Second Course on Ordinal Analysis
Logic
2022-08-11 v2
Abstract
These lecture notes introduce central notions of impredicative ordinal analysis, such as the Bachmann-Howard ordinal and the method of collapsing, which transforms uncountable proof trees into countable ones. Specifically, we analyze parameter-free -comprehension and show that it cannot prove the extended Kruskal theorem due to Harvey Friedman (not even for two labels). In terms of prerequisites, we build on a previous lecture on the ordinal analysis of Peano arithmetic. The present material is intended for 12 lectures and 6 exercise sessions of 90 minutes each.
Keywords
Cite
@article{arxiv.2204.09321,
title = {Impredicativity and Trees with Gap Condition: A Second Course on Ordinal Analysis},
author = {Anton Freund},
journal= {arXiv preprint arXiv:2204.09321},
year = {2022}
}