2022/04/20 by Freund, Anton
#03-01 #03B30 #03F05 #03F15 #03F35 #03F40 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2204.09321
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 Π11-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.