\begin{definition}[Definition:Ring of Sets/Definition 3]
A '''ring of sets''' $\RR$ is a system of sets with the following properties:
{{begin-axiom}}
{{axiom | n = \text {RS} 1_3
        | lc= Empty Set:
        | m = \O \in \RR
}}
{{axiom | n = \text {RS} 2_3
        | lc= Closure under Set Difference:
        | q = \forall A, B \in \RR
        | m = A \setminus B \in \RR
}}
{{axiom | n = \text {RS} 3_3
        | lc= Closure under Disjoint Union:
        | q = \forall A, B \in \RR
        | m = A \cap B = \O \implies A \cup B \in \RR
}}
{{end-axiom}}
\end{definition}