\begin{definition}[Definition:Sigma-Ring/Definition 3]
A '''$\sigma$-ring''' $\Sigma$ is a system of sets with the following properties:
{{begin-axiom}}
{{axiom | n = \text {SR} 1'
        | lc= Empty Set:
        | m = \O \in \Sigma
}}
{{axiom | n = \text {SR} 2'
        | lc= Closure under Set Difference:
        | q = \forall A, B \in \Sigma
        | m = A \setminus B \in \Sigma
}}
{{axiom | n = \text {SR} 3'
        | lc= Closure under Countable Disjoint Unions:
        | q = \forall A_n \in \Sigma: n = 1, 2, \ldots
        | m = \bigsqcup_{n \mathop = 1}^\infty A_n \in \Sigma
}}
{{end-axiom}}
\end{definition}