The Rigid Relation Principle, a New Weak Choice Principle
Logic
2011-06-24 v1
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 (among other general instances) is provable without the axiom of choice.
Keywords
Cite
@article{arxiv.1106.4635,
title = {The Rigid Relation Principle, a New Weak Choice Principle},
author = {Joel David Hamkins and Justin Palumbo},
journal= {arXiv preprint arXiv:1106.4635},
year = {2011}
}