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math.LO2019
Linear extenders and the Axiom of Choice
Marianne Morillon
In set theory without the axiom of Choice ZF, we prove that for every commutative field IK, the following statement D_{\IK}: "On every non null IK-vector space, there exists a non…
math.LO2019
Multiple Choices imply the Ingleton and Krein-Milman axioms
Marianne Morillon
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…