On rigid relation principles in set theory without the axiom of choice
Volume 232 / 2016
Fundamenta Mathematicae 232 (2016), 199-226
MSC: Primary 03E25; Secondary 03E35.
DOI: 10.4064/fm960-12-2015
Published online: 21 December 2015
Abstract
We study the deductive strength of the following statements:
$\mathsf{RR}$: every set has a rigid binary relation,
$\mathsf{HRR}$: every set has a hereditarily rigid binary relation,
$\mathsf{SRR}$: every set has a strongly rigid binary relation,
in set theory without the Axiom of Choice. $\mathsf{RR}$ was recently formulated by J. D. Hamkins and J. Palumbo, and $\mathsf{SRR}$ is a classical (non-trivial) $\mathsf{ZFC}$-result by P. Vopěnka, A. Pultr and Z. Hedrlín.
