The Rigid Relation Principle, a New Weak Choice Principle

Details The Rigid Relation Principle, a New Weak Choice Principle The Rigid Relation Principle, a New Weak Choice Principle

2011-06-23

arxiv.org/abs/1106.4635v1

Mathematics

Logic

Scientific paper

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.

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