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Are there any particular term for a pair $(U;A)$ where $U$ is a set and $A\in\mathscr{P}U$? That is, saying informally, $(U;A)$ is a set $A$ together with a set $U$ on which $A$ is defined ($A$ is defined as a subset of $U$).

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    One could consider this pair as the inclusion $A\subset U$...2012-05-20
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    How about *extension*? But I don't think there is a standard term for that. The closer I know of is [pointed set](http://en.wikipedia.org/wiki/Pointed_set).2012-05-20
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    You could call it a structure with one unary relation, or simply a unary relation $A$ on $U$.2012-10-12

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