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2019 Abstraction Principles and the Classification of Second-Order Equivalence Relations
Sean C. Ebels-Duggan
Notre Dame J. Formal Logic 60(1): 77-117 (2019). DOI: 10.1215/00294527-2018-0023

Abstract

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 second-order 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.

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Sean C. Ebels-Duggan. "Abstraction Principles and the Classification of Second-Order Equivalence Relations." Notre Dame J. Formal Logic 60 (1) 77 - 117, 2019. https://doi.org/10.1215/00294527-2018-0023

Information

Received: 9 March 2016; Accepted: 3 November 2016; Published: 2019
First available in Project Euclid: 25 January 2019

zbMATH: 07060309
MathSciNet: MR3911107
Digital Object Identifier: 10.1215/00294527-2018-0023

Subjects:
Primary: 03A05
Secondary: 00A30, 03B15

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 1 • 2019
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