THE SET-THEORETIC MULTIVERSE
THE SET-THEORETIC MULTIVERSE
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集合论多元宇宙
DOI：
10.1017/s1755020311000359
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Hamkins
中科院分区：
文献类型：
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作者：
J. Hamkins
摘要本文介绍和论证的集合论中的多元宇宙观点是这样的观点：存在许多不同的集合概念，每个概念都在相应的集合论宇宙中实例化。相反，宇宙观认为存在一个绝对的背景集合概念，以及一个相应的绝对集合论宇宙，其中每个集合论问题都有一个确定的答案。我认为，多元宇宙的立场解释了我们对大量集合论可能性的经验，这一现象挑战了宇宙观。特别是，我认为，连续统假设是解决了我们的广泛知识，它如何在多元宇宙中的行为的多元宇宙的观点，因此，它不能再解决以前希望的方式。
Abstract The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer. The multiverse position, I argue, explains our experience with the enormous range of set-theoretic possibilities, a phenomenon that challenges the universe view. In particular, I argue that the continuum hypothesis is settled on the multiverse view by our extensive knowledge about how it behaves in the multiverse, and as a result it can no longer be settled in the manner formerly hoped for.