A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice
Logic
2007-05-23 v1
Abstract
In this paper I present an (\in, =)-sentence, AC**, with only 5 quantifiers, that logically implies the axiom of choice, AC. Furthermore, using a weak fragment of ZF set theory, I prove that AC implies AC**. Up to now 6 quantifiers were the minimum and 3 quantifiers don't suffice since all 3-quantifier (\in, =)-sentences are decided in a weak fragment of ZF set theory. Thus the gap is reduced to the undecided case of a 4 quantifier sentence ZF-equivalent to AC.
Keywords
Cite
@article{arxiv.0705.3162,
title = {A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice},
author = {Kurt Maes},
journal= {arXiv preprint arXiv:0705.3162},
year = {2007}
}
Comments
9 pages