Abstraction principles and the classification of second-order equivalence relations

Sean C. Ebels-Duggan*

*Corresponding author for this work

Research output: Contribution to journalArticle

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 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 languageEnglish (US)
Pages (from-to)77-117
Number of pages41
JournalNotre Dame Journal of Formal Logic
Volume60
Issue number1
DOIs
Publication statusPublished - Jan 1 2019

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Keywords

  • Abstraction
  • Categoricity
  • Equivalence relations
  • Neologicism
  • Second-order logic

ASJC Scopus subject areas

  • Logic

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