Multiple Choices imply the Ingleton and Krein-Milman axioms
Logic
2019-01-15 v1
Abstract
In set theory without the Axiom of Choice, we consider Ingleton's axiom which is the counterpart in ultrametric analysis of the Hahn-Banach axiom. We show that in , set theory without the Axiom of Choice weakened to allow "atoms", Ingleton's axiom does not imply the Axiom of Choice (this solves in a question raised by van Rooij (1992). We also prove that in , the "multiple Choice" axiom implies the Krein-Milman axiom. We deduce that, in , the conjunction of the Hahn-Banach, Ingleton and Krein-Milman axioms does not imply the Axiom of Choice.
Keywords
Cite
@article{arxiv.1901.04021,
title = {Multiple Choices imply the Ingleton and Krein-Milman axioms},
author = {Marianne Morillon},
journal= {arXiv preprint arXiv:1901.04021},
year = {2019}
}