View source for Prime ideal theorem

The assertion that every ideal in a [[Boolean algebra]] can be extended to a prime ideal.  It is a consequence of the [[Axiom of Choice]], but is known to be strictly weaker.  It implies the [[Tikhonov theorem]] for Hausdorff spaces.

====References====
* T. Jech, "Set theory. The third millennium edition, revised and expanded" Springer Monographs in Mathematics (2003). ISBN 3-540-44085-2 {{ZBL|1007.03002}}