Hereditary system of sets

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Needs linking to where it is used, notes on a sort of "power-set" like construct.

Note: see hereditary for different uses of the word, this page refers to hereditary as used in Measure Theory and Hereditary (measure theory) redirects here

Definition

A collection of sets, [ilmath]\mathcal{H} [/ilmath] is said to be hereditary if:

• [ilmath]\forall A\in\mathcal{H}\forall B\in\mathcal{P}(A)[B\in\mathcal{H}][/ilmath], in words:
  • for all sets [ilmath]A\in\mathcal{H} [/ilmath] all subsets of [ilmath]A[/ilmath] must be in [ilmath]\mathcal{H} [/ilmath]

See also

• Hereditary [ilmath]\sigma[/ilmath]-ring - the motivation for this definition.