The rigid relation principle, a new weak choice principle

Mathematical Logic Quarterly 58 (6):394-398 (2012)
  Copy   BIBTEX

Abstract

The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom of choice nor provable in Zermelo-Fraenkel set theory without the axiom of choice. Thus, it is a new weak choice principle. Nevertheless, the restriction of the principle to sets of reals is provable without the axiom of choice

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,100

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

In Search of a Pointless Decision Principle.Prasanta S. Bandyopadhayay - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:260 - 269.
Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
Infinite utilitarianism: More is always better.Luc Lauwers & Peter Vallentyne - 2004 - Economics and Philosophy 20 (2):307-330.
A closer look at the 'new' principle.Michael Strevens - 1995 - British Journal for the Philosophy of Science 46 (4):545-561.
R and Relevance Principle Revisited.Eunsuk Yang - 2013 - Journal of Philosophical Logic 42 (5):767-782.
The axiom of choice.John L. Bell - 2008 - Stanford Encyclopedia of Philosophy.
Formulating the Precautionary Principle.Neil A. Manson - 2002 - Environmental Ethics 24 (3):263-274.

Analytics

Added to PP
2013-10-31

Downloads
61 (#264,402)

6 months
9 (#311,219)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Joel David Hamkins
Oxford University

Citations of this work

Possible Patterns.Jeffrey Sanford Russell & John Hawthorne - 2018 - Oxford Studies in Metaphysics 11.

Add more citations

References found in this work

The Axiom of Choice.Thomas J. Jech - 1973 - Amsterdam, Netherlands: North-Holland.
Ramsey's theorem in the hierarchy of choice principles.Andreas Blass - 1977 - Journal of Symbolic Logic 42 (3):387-390.

Add more references