抽象原则与二阶等价关系的分类
Abstraction Principles and the Classification of Second-Order Equivalence Relations
摘要：
本文改进了新逻辑主义数学哲学家感兴趣的两个已有定理。第一个是分类定理，由于罚款的等价关系之间的概念定义在一个良好的行为二阶逻辑。改进的定理指出，如果等价关系$E$的定义没有非逻辑词汇，那么任何等价类的二叉切片--那些具有等量补集的等价类的等量元素--只能有三个轮廓之一。对Fine定理的改进允许对抽象原则下行为良好的模型进行分析，这反过来又导致了Walsh和Ebels-Duggan的相对范畴性定理的改进。
英文摘要：
This paper improves two existing theorems of interest to neo-logicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic. The improved theorem states that if an equivalence relation $E$ is defined without non-logical vocabulary, then the bicardinal slice of any equivalence class---those equinumerous elements of the equivalence class with equinumerous complements---can have one of only three profiles. The improvements to Fine's theorem allow for an analysis of the well-behaved models had by an abstraction principle, and this in turn leads to an improvement of Walsh and Ebels-Duggan's relative categoricity theorem.
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