The ground axiom
The ground axiom
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基本公理
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Jonas Reitz
中科院分区：
文献类型：
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作者：
Jonas Reitz
摘要 提出了一个新的公理，即基本公理，断言宇宙不是一个迫使任何内部模型扩展的非平凡集合。 Ground Axiom 是一阶可表达的，并且任何 ZFC 模型都有一个满足它的类强制扩展。基本公理独立于许多著名的集合论断言，包括广义连续统假说、每个集合都是序数可定义的断言 V=HOD，以及可测基数和超紧基数的存在。相关的基岩公理断言宇宙是满足基本公理的模型的强制外延的集合，也是一阶可表达的，并且其否定是一致的。
Abstract A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion V=HOD that every set is ordinal definable, and the existence of measurable and supercompact cardinals. The related Bedrock Axiom, asserting that the universe is a set forcing extension of a model satisfying the Ground Axiom, is also first-order expressible, and its negation is consistent.