A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice
| dc.creator | Maes, Kurt | |
| dc.date | 2007-05-22 | |
| dc.date.accessioned | 2026-07-07T08:02:50Z | |
| dc.date.available | 2026-07-07T08:02:50Z | |
| dc.description | 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. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/0705.3162 | |
| dc.identifier | http://arxiv.org/abs/0705.3162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129359 | |
| dc.subject | Logic | |
| dc.subject | 03E25; 03E30 | |
| dc.title | A 5-quantifier (\in,=)-expression ZF-equivalent to the Axiom of Choice | |
| dc.type | text |