Total order in the power set of the real line

Question

Is it possible to define constructively a total order in the power set of the real line ?

score 3 · Accepted Answer · edited Apr 13 '17 at 12:58

3

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.

edited Apr 13 '17 at 12:58

Community

answered Jun 16 '12 at 18:59

Asaf Karagila

1 Answers1