Definition:Algebra of Sets/Definition 1

Definition
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 $S$ $\RR$ satisfies the algebra of sets axioms:

Also see

 * Equivalence of Definitions of Algebra of Sets