Structure (mathematical logic)
Domain

The domain of a structure is an arbitrary set; it is also called the underlying set of the structure, its carrier (especially in universal algebra), its universe (especially in model theory, cf. universe), or its domain of discourse. In classical first-order logic, the definition of a structure prohibits the empty domain.

Sometimes the notation dom (A) {\displaystyle \operatorname {dom} ({\mathcal {A}})} or | A | {\displaystyle |{\mathcal {A}}|} is used for the domain of A, {\displaystyle {\mathcal {A}},} but often no notational distinction is made between a structure and its domain (that is, the same symbol A {\displaystyle {\mathcal {A}}} refers both to the structure and its domain.)
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