不确定性与带间隙条件的树：序分析第二课
Impredicativity and Trees with Gap Condition: A Second Course on Ordinal Analysis
摘要：
这些课堂讲稿介绍了非谓词序数分析的中心概念，例如Bachmann-Howard序数和折叠方法，该方法将不可数的证明树转换为可数的证明树。具体来说，我们分析参数自由$Π^1_1$ -理解，并表明，它不能证明扩展Kruskal定理，由于哈维弗里德曼（甚至没有两个标签）。在先决条件方面，我们建立在以前的讲座上皮亚诺算术的序数分析。本教材拟用于12次讲座和6次练习，每次90分钟。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
