Abstraction principles and the classification of second-order equivalence relations

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
StatePublished - Jan 1 2019

Fingerprint

Order Relation
Equivalence relation
Theorem
Equivalence class
Second-order Logic
Slice
Complement
Abstraction

Keywords

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

ASJC Scopus subject areas

  • Logic

Cite this

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Abstraction principles and the classification of second-order equivalence relations. / Ebels Duggan, Sean Christopher.

In: Notre Dame Journal of Formal Logic, Vol. 60, No. 1, 01.01.2019, p. 77-117.

Research output: Contribution to journalArticle

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