Diaconescu's theorem shows Choice can be derived from seemingly innocuous structural assumptions, meaning the supporting argument may smuggle in Choice rather than isolate well-foundedness as the operative factor.

?Rate how convincing each reason is below to see the overall strength.

No one has weighed in yet. Be the first to share reasons for or against this statement.

Axiom of Choice(Foundations of mathematics; arises in second-order logic as the statement that every total binary relation has a choice function): Given a set A of non-empty pairwise disjoint sets, there exists a set B containing exactly one element from each set in A. When A is infinite, forming B requires making infinitely many simultaneous choices.
Diaconescu's theorem(as used in logic and mathematics): A mathematical proof discovered by Romanian logician Radu Diaconescu showing that a certain logical principle (the Axiom of Choice) can be proven true using other basic assumptions, even though those assumptions seem unrelated to it.
Smuggle in (philosophical usage)(as used in logic and philosophy): To sneak in an assumption or conclusion that isn't obviously there, so that an argument appears simpler or more neutral than it actually is.
Structural assumptions(as used in logic and philosophy)

Based on where you are in your exploration