# Category:Algebras of Sets

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This category contains results about **Algebras of Sets**.

Definitions specific to this category can be found in Definitions/Algebras of Sets.

Let $S$ be a set.

Let $\powerset S$ be the power set of $S$.

Let $\RR \subseteq \powerset S$ be a set of subsets of $S$.

$\RR$ is an **algebra of sets over $S$** if and only if $\RR$ satisfies the algebra of sets axioms:

\((\text {AS} 1)\) | $:$ | Unit: | \(\ds S \in \RR \) | ||||||

\((\text {AS} 2)\) | $:$ | Closure under Union: | \(\ds \forall A, B \in \RR:\) | \(\ds A \cup B \in \RR \) | |||||

\((\text {AS} 3)\) | $:$ | Closure under Complement Relative to $S$: | \(\ds \forall A \in \RR:\) | \(\ds \relcomp S A \in \RR \) |

## Subcategories

This category has the following 5 subcategories, out of 5 total.

### A

### S

## Pages in category "Algebras of Sets"

The following 9 pages are in this category, out of 9 total.