On rigid relation principles in set theory without the axiom of choice
Paul Howard; Eleftherios Tachtsis
Fundamenta Mathematicae (2016)
- Volume: 232, Issue: 3, page 199-226
- ISSN: 0016-2736
Access Full Article
top
Abstract
topHow to cite
topPaul Howard, and Eleftherios Tachtsis. "On rigid relation principles in set theory without the axiom of choice." Fundamenta Mathematicae 232.3 (2016): 199-226. <http://eudml.org/doc/286354>.
@article{PaulHoward2016,
abstract = {
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.
},
author = {Paul Howard, Eleftherios Tachtsis},
journal = {Fundamenta Mathematicae},
keywords = {axiom of choice; weak choice principles; rigid binary relation; hereditarily rigid binary relation; strongly rigid binary relation; permutation models of ZFA; symmetric models of ZF},
language = {eng},
number = {3},
pages = {199-226},
title = {On rigid relation principles in set theory without the axiom of choice},
url = {http://eudml.org/doc/286354},
volume = {232},
year = {2016},
}
TY - JOUR
AU - Paul Howard
AU - Eleftherios Tachtsis
TI - On rigid relation principles in set theory without the axiom of choice
JO - Fundamenta Mathematicae
PY - 2016
VL - 232
IS - 3
SP - 199
EP - 226
AB -
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.
LA - eng
KW - axiom of choice; weak choice principles; rigid binary relation; hereditarily rigid binary relation; strongly rigid binary relation; permutation models of ZFA; symmetric models of ZF
UR - http://eudml.org/doc/286354
ER -
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.