A 5-quantifier (in,=)-expression ZF-equivalent to the Axiom of Choice - Mathematics > Logic

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 weakfragment of ZF set theory, I prove that AC implies AC**.Up to now 6 quantifiers were the minimum and 3 quantifiers don-t sufficesince all 3-quantifier (\in, =)-sentences are decided in a weak fragment of ZFset theory. Thus the gap is reduced to the undecided case of a 4 quantifiersentence ZF-equivalent to AC.

Author: Kurt Maes

Source: https://arxiv.org/