Is it fundamentally wrong to think if the Axiom of Choice (AC) as a logical codification of indeterminism? Could it not be related to matching distributions with a random number generator?
2026-04-08 06:29:39.1775629779
Is Axiom of Choice related to Indeterminism
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Yes. It's wrong.
The axiom of choice is not choosing "random elements". That's what existential instantiation is doing, in some sense. The axiom of choice is best understood in some sense in a constructive framework: if you can choose an element from each set in a family of sets, then you're supposedly able to do it uniformly.
Of course, in classical mathematics this is not true, but the axiom of choice lets you overcome that issue.
The "non-constructive part" of the axiom of choice is really an artifact of existential instantiation, if you think about it, that's the part moving from "there is a choice function" to "$f$ is a choice function".