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The rigid relation principle, a new weak choice principle
Author(s) -
Hamkins Joel David,
Palumbo Justin
Publication year - 2012
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201100081
Subject(s) - axiom of choice , mathematics , zermelo–fraenkel set theory , axiom , urelement , binary relation , constructive set theory , relation (database) , set theory , mathematical economics , set (abstract data type) , discrete mathematics , pure mathematics , geometry , computer science , database , programming language
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.