论文标题
钢铁计划：证据框架，核心和终极L
Steel's Programme: Evidential Framework, the Core and Ultimate-L
论文作者
论文摘要
我们解决了Steel的计划，以确定一个“首选”集合理论的宇宙，以及使用其多宇宙公理MV和“核心假设”来扩展ZFC的最佳公理。在第一部分中，我们检查了MV的证据框架，特别是通过强迫“代表” ZFC的替代扩展而获得的大型红衣主教和“世界”的使用。在第二部分中，我们解决了MV_T核心的存在和可能的特征（其中T为ZFC+大型红衣主教）。在最后一部分中，我们讨论了核心是终极l的假设，并检查了核心大学是否以及如何以及如何证明V = ultimate-l是ZFC的最佳（和最终）扩展。为此，我们考虑了几种策略，并根据MV的证据框架评估了他们的前景。
We address Steel's Programme to identify a 'preferred' universe of set theory and the best axioms extending ZFC by using his multiverse axioms MV and the 'core hypothesis'. In the first part, we examine the evidential framework for MV, in particular the use of large cardinals and of 'worlds' obtained through forcing to 'represent' alternative extensions of ZFC. In the second part, we address the existence and the possible features of the core of MV_T (where T is ZFC+Large Cardinals). In the last part, we discuss the hypothesis that the core is Ultimate-L, and examine whether and how, based on this fact, the Core Universist can justify V=Ultimate-L as the best (and ultimate) extension of ZFC. To this end, we take into account several strategies, and assess their prospects in the light of MV's evidential framework.
