Is it possible to define constructively a total order in the power set of the real line ?
Total order in the power set of the real line
4
$\begingroup$
set-theory
axiom-of-choice
1 Answers
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You don't. It is consistent with ZF that there is no linear ordering of $\mathcal P(\mathbb R)$.
Andres Caicedo wrote a rather detailed answer to this on this MathOverflow thread.