# Category:Examples of Use of Boolean Prime Ideal Theorem

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

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

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:

- $P \cap F = \O$

## Pages in category "Examples of Use of Boolean Prime Ideal Theorem"

The following 22 pages are in this category, out of 22 total.

### C

- Compact Subspace of Linearly Ordered Space/Reverse Implication
- Compact Subspace of Linearly Ordered Space/Reverse Implication/Proof 2
- Compactness Theorem/Proof using Consistency Principle
- Compactness Theorem/Proof using Gödel's Completeness Theorem
- Consistency Principle for Binary Mess
- Cowen-Engeler Lemma