Notre Dame Journal of Formal Logic 60 (1):77-117 (2019)

Authors
Sean Ebels-Duggan
Northwestern University
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.
Keywords abstraction   categoricity   equivalence relations   second-order logic  neologicism
Categories (categorize this paper)
DOI 10.1215/00294527-2018-0023
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,267
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.
Logical Operations.Vann McGee - 1996 - Journal of Philosophical Logic 25 (6):567 - 580.
Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
New V, ZF and Abstraction.Stewart Shapiro & Alan Weir - 1999 - Philosophia Mathematica 7 (3):293-321.

View all 16 references / Add more references

Citations of this work BETA

Identifying Finite Cardinal Abstracts.Sean C. Ebels-Duggan - 2021 - Philosophical Studies 178 (5):1603-1630.

Add more citations

Similar books and articles

The Strength of Abstraction with Predicative Comprehension.Sean Walsh - 2016 - Bulletin of Symbolic Logic 22 (1):105–120.
Abstraction Relations Need Not Be Reflexive.Jonathan Payne - 2013 - Thought: A Journal of Philosophy 2 (2):137-147.
Relative Categoricity and Abstraction Principles.Sean Walsh & Sean Ebels-Duggan - 2015 - Review of Symbolic Logic 8 (3):572-606.
On Polynomial-Time Relation Reducibility.Su Gao & Caleb Ziegler - 2017 - Notre Dame Journal of Formal Logic 58 (2):271-285.
? 0 N -Equivalence Relations.Andrea Sorbi - 1982 - Studia Logica 41 (4):351-358.
Abductive Equivalence in First-Order Logic.Katsumi Inoue & Chiaki Sakama - 2006 - Logic Journal of the IGPL 14 (2):333-346.
Maximal R.E. Equivalence Relations.Jeffrey S. Carroll - 1990 - Journal of Symbolic Logic 55 (3):1048-1058.
A Strengthening of the Caesar Problem.Joongol Kim - 2011 - Erkenntnis 75 (1):123-136.
Classifying Positive Equivalence Relations.Claudio Bernardi & Andrea Sorbi - 1983 - Journal of Symbolic Logic 48 (3):529-538.
$\sum_{0}^{N}$ -Equivalence Relations.Andrea Sorbi - 1982 - Studia Logica 41 (4):351 - 358.
Thin Equivalence Relations and Effective Decompositions.Greg Hjorth - 1993 - Journal of Symbolic Logic 58 (4):1153-1164.
Fraenkel–Carnap Questions for Equivalence Relations.George Weaver & Irena Penev - 2011 - Australasian Journal of Logic 10:52-66.
Superrigidity and Countable Borel Equivalence Relations.Simon Thomas - 2003 - Annals of Pure and Applied Logic 120 (1-3):237-262.

Analytics

Added to PP index
2019-01-25

Total views
18 ( #590,901 of 2,455,894 )

Recent downloads (6 months)
2 ( #303,388 of 2,455,894 )

How can I increase my downloads?

Downloads

My notes