具有真类不可辨元的集合论
逻辑
2022-03-11 v4
摘要
我们研究 ZFC 集合论（在扩展语言中）的一种扩展，该扩展规定宇宙上存在一真类不可辨元。本文的主要结果之一表明，该 ZFC 扩展的纯集合论推论与通过向 ZFC 增添（Levy）概型所得集合论系统的定理一致，其中该概型的实例对元理论中的每个自然数 断言：存在一个 -Mahlo 基数 ，使得由 决定的宇宙初始段是宇宙的 -初等子模型。
引用
@article{arxiv.2008.07706,
title = {Set theory with a proper class of indiscernibles},
author = {Ali Enayat},
journal= {arXiv preprint arXiv:2008.07706},
year = {2022}
}
备注
35 pages. This version corrects some minor issues detected in the previous draft, and includes refinements of certain results (see Theorem 4.1 and Remark 6.6). Note that a section dealing with models of Peano arithmetic has been excised from this draft (a much expanded version of it will appear as a separate paper)