Re: Equivalent to Axiom of Choice?

Thomas Andrews wrote:

Theorem: Every partially ordered set can be extended to a total order.

The easy proof I've found of this uses the axiom of choice (well,
specifically, Zorn's Lemma.)

Is it equivalent to the axiom of choice?


no, it does not even imply that every Boolean algebra has a prime ideal. See

http://citeseer.ist.psu.edu/87611.html


--
Stefan Wehmeier
stefanw@xxxxxxxxxxx

.

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