An ordinal analysis of stability
An ordinal analysis of stability
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稳定性的顺序分析
DOI：
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发表时间：
2005
影响因子：
0.3
通讯作者：
M. Rathjen
中科院分区：
文献类型：
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作者：
M. Rathjen
摘要：本文是一系列三篇文章中的第一篇，最后以12- 12理解的顺序分析为高潮。在集合论方面，Kripke-Platek集合论，KP，加上Kripke-Platek 1-分离，对应于Kripke-Platek集合论。后一种理论的力量在于它证明了序数π的存在，使得对于所有β>π，π是β-稳定的，即Lπ是Lβ的一个π 1-初等子结构。本文的目的是对不太复杂的稳定性关系的场景进行序分析，因为经验表明，首先解释某些较简单的情况将大大有助于理解Π12-理解的序分析。本文介绍了一种基于ν-不可描述的基数的序表示系统，然后使用该系统来确定证明的上界-理论的理论强度KPi+ ρ ππ是π+ρ-稳定的，其中KPi是KP通过公理“每个集合都包含在一个容许集合中”来扩充的。
Abstract.This paper is the first in a series of three which culminates in an ordinal analysis of Π12-comprehension. On the set-theoretic side Π12-comprehension corresponds to Kripke-Platek set theory, KP, plus Σ1-separation. The strength of the latter theory is encapsulated in the fact that it proves the existence of ordinals π such that, for all β>π, π is β-stable, i.e. Lπ is a Σ1-elementary substructure of Lβ. The objective of this paper is to give an ordinal analysis of a scenario of not too complicated stability relations as experience has shown that the understanding of the ordinal analysis of Π12-comprehension is greatly facilitated by explicating certain simpler cases first.This paper introduces an ordinal representation system based on ν-indescribable cardinals which is then employed for determining an upper bound for the proof–theoretic strength of the theory KPi+ ∀ρ ∃ππ is π+ρ-stable, where KPi is KP augmented by the axiom saying that every set is contained in an admissible set.