We study the deductive strength of the following statements: 𝖱𝖱: every set has a rigid binary relation, 𝖧𝖱𝖱: every set has a hereditarily rigid binary relation, 𝖲𝖱𝖱: every set has a strongly rigid binary relation, in set theory without the Axiom of Choice. 𝖱𝖱 was recently formulated by J. D. Hamkins and J. Palumbo, and 𝖲𝖱𝖱 is a classical (non-trivial) 𝖹𝖥𝖢-result by P. Vopěnka, A. Pultr and Z. Hedrlín.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm960-12-2015,
author = {Paul Howard and Eleftherios Tachtsis},
title = {On rigid relation principles in set theory without the axiom of choice},
journal = {Fundamenta Mathematicae},
volume = {233},
year = {2016},
pages = {199-226},
zbl = {06545383},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm960-12-2015}
}
Paul Howard; Eleftherios Tachtsis. On rigid relation principles in set theory without the axiom of choice. Fundamenta Mathematicae, Tome 233 (2016) pp. 199-226. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm960-12-2015/