Abstraction Principles and the Classification of Second-Order Equivalence Relations

  title={Abstraction Principles and the Classification of Second-Order Equivalence Relations},
  author={Sean Ebels-Duggan},
  journal={Notre Dame J. Formal Log.},
  • Sean Ebels-Duggan
  • Published 2019
  • Mathematics, Computer Science
  • Notre Dame J. Formal Log.
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… Expand
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