Category:Examples of Use of Boolean Prime Ideal Theorem

This category contains examples of use of Boolean Prime Ideal Theorem.

Let $\struct {S, \le}$ be a Boolean lattice.

Let $I$ be an ideal in $S$.

Let $F$ be a filter on $S$.

Let $I \cap F = \O$.

Then there exists a prime ideal $P$ in $S$ such that:

$I \subseteq P$

and:

$P \cap F = \O$