论文标题
障碍性和差距条件的树木：序数分析的第二个课程
Impredicativity and Trees with Gap Condition: A Second Course on Ordinal Analysis
论文作者
论文摘要
这些讲义介绍了不可思议的序数分析的中心概念，例如Bachmann-Howard序数和崩溃方法，将无数的证明树转化为可数的树。具体而言，我们分析了无参数$π^1_1 $ - 概述，并表明它无法证明由于Harvey Friedman（甚至不适合两个标签）引起的扩展的Kruskal定理。就先决条件而言，我们基于先前关于Peano算术的序数分析的讲座。目前的材料旨在进行12个讲座和6次练习90分钟。
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 $Π^1_1$-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.
