This article improves two existing theorems of interest to neologicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved secondorder logic. The improved theorem states that if an equivalence relation E is defined without nonlogical 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.
|Original language||English (US)|
|Number of pages||41|
|Journal||Notre Dame Journal of Formal Logic|
|State||Published - 2019|
- Equivalence relations
- Second-order logic
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