# ZF Set Theory and Law of the Excluded Middle

1. Oct 11, 2014

### HJ Farnsworth

Hello,

I know that the law of the excluded middle is implied in ZFC set theory, since it is implied by the axiom of choice. Taking away the axiom of choice, does ZF set theory (with axioms as stated in the Wikipedia article http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory), imply the law of the excluded middle [for infinite sets]?

If LEM does follow from ZF, could you please provide the proof if you know it, or point me to the proof if you know where it is, or tell me what ZF axioms it follows from if you don't know of theproof or its location?

Thanks very much.

-HJ Farnsworth

2. Oct 12, 2014