论文标题
大型基本一致性强度的层次结构的非线性和不良性
Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength
论文作者
论文摘要
许多人将理论家指出了一致性强度的层次结构的线性现象，通过这种现象，自然理论倾向于线性排序，并且确实通过一致性强度井井有条。为什么要线性？在本文中，我介绍了反例，在大型基本一致性强度的层次结构中，非线性和不良性的自然实例，自然或自然而然地自然而然。我提出了ZFC和大型红衣主教理论的各种谨慎的列举，这些理论在一致性强度方面表现出无与伦比的和不可能的，但我认为，自然是自然的。我认为“自然”在线性现象中所扮演的哲学角色，最终认为我们应该放弃空虚的自然谈话，而旨在使我们发现所需的数学和逻辑特征精确。
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I present counterexamples, natural instances of nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength, as natural or as nearly natural as I can make them. I present diverse cautious enumerations of ZFC and large cardinal set theories, which exhibit incomparability and illfoundedness in consistency strength, and yet, I argue, are natural. I consider the philosophical role played by "natural" in the linearity phenomenon, arguing ultimately that we should abandon empty naturality talk and aim instead to make precise the mathematical and logical features we had found desirable.
