Hereditary sigma-ring generated by

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Definition

Given a system of sets, $S$, the hereditary $\sigma$-ring generated by $S$ is:

• The smallest hereditary $\sigma$-ring containing $S$

We denote this $\mathcal{H}_{\sigma R}(S)$

Claims

• $\mathcal{H}(\sigma_R(S))=\sigma_R(\mathcal{H}(S))$ - see Notes:Hereditary sigma-ring

See also

• Hereditary system generated by