多重宇宙视角下的可构造性公理
逻辑
2012-10-25 v1
摘要
本文将论证，普遍持有的通过最大化原则得出 的立场（即基于限制性理由拒绝可构造性公理 ），实际上通过预设一个绝对的序数背景概念，在集合论哲学的多元论辩论中隐含地采取了某种立场。相比之下，在集合具有向上可扩展概念的视角下，鉴于各种事实表明集合论模型通常可以在更大的集合论宇宙内扩展为 的模型，该论证似乎失去了其效力。
引用
@article{arxiv.1210.6541,
title = {A multiverse perspective on the axiom of constructiblity},
author = {Joel David Hamkins},
journal= {arXiv preprint arXiv:1210.6541},
year = {2012}
}
备注
21 pages. This article expands on an argument that I made during my talk at the Asian Initiative for Infinity: Workshop on Infinity and Truth, held July 25--29, 2011 at the Institute for Mathematical Sciences, National University of Singapore. Commentary concerning this paper can be made at http://jdh.hamkins.org/multiverse-perspective-on-constructibility