Mathematical Objects arising from Equivalence Relations and their Implementation in Quine's NF

Philosophia Mathematica 24 (1):50-59 (2016)
  Copy   BIBTEX

Abstract

Many mathematical objects arise from equivalence classes and invite implementation as those classes. Set-existence principles that would enable this are incompatible with ZFC's unrestricted _aussonderung_ but there are set theories which admit more instances than does ZF. NF provides equivalence classes for stratified relations only. Church's construction provides equivalence classes for "low" sets, and thus, for example, a set of all ordinals. However, that set has an ordinal in turn which is not a member of the set constructed; so no set of _all_ ordinals is obtained thereby. This "recurrence problem" is discussed.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On Σ1 1 equivalence relations with Borel classes of bounded rank.Ramez L. Sami - 1984 - Journal of Symbolic Logic 49 (4):1273 - 1283.
Thin equivalence relations and inner models.Philipp Schlicht - 2014 - Annals of Pure and Applied Logic 165 (10):1577-1625.
Thin equivalence relations and effective decompositions.Greg Hjorth - 1993 - Journal of Symbolic Logic 58 (4):1153-1164.
Labelling classes by sets.M. Victoria Marshall & M. Gloria Schwarze - 2005 - Archive for Mathematical Logic 44 (2):219-226.
Isomorphism Testing For Equivalence Relations.Edward Szczypka - 1996 - Reports on Mathematical Logic:101-109.
Some applications of illfoundedness.Greg Hjorth - 1996 - Archive for Mathematical Logic 35 (3):131-144.
On Bounded Type-Definable Equivalence Relations.Ludomir Newelski & Krzysztof Krupi?Ski - 2002 - Notre Dame Journal of Formal Logic 43 (4):231-242.
Superrigidity and countable Borel equivalence relations.Simon Thomas - 2003 - Annals of Pure and Applied Logic 120 (1-3):237-262.
Classes of Markov-like k-ALGORITHMS.Zdzislaw Grodzki & Jerzy Mycka - 1996 - Reports on Mathematical Logic:83-99.
Continuous versus Borel reductions.Simon Thomas - 2009 - Archive for Mathematical Logic 48 (8):761-770.

Analytics

Added to PP
2016-04-13

Downloads
14 (#846,545)

6 months
2 (#668,348)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Thomas Forster
Cambridge University

Citations of this work

Frege's Cardinals and Neo-Logicism.Roy T. Cook - 2016 - Philosophia Mathematica 24 (1):60-90.
Paolo Mancosu.*Abstraction and Infinity. [REVIEW]Roy T. Cook & Michael Calasso - 2019 - Philosophia Mathematica 27 (1):125-152.

Add more citations

References found in this work

No references found.

Add more references