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

Details A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice

2007-05-22

arxiv.org/abs/0705.3162v1

Mathematics

Logic

9 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-416041