= Embedding of first-order structures
{title2=$e:A\hookrightarrow B$}
= First-order-structure embedding
{synonym}
An <embedding of first-order structures> is an <injective> <function> preserving <function symbols> and constants and both preserving and reflecting every relation symbol. Its image is a <substructure>. Satisfaction of an atomic <diagram of a structure> in an expansion gives such an <embedding of first-order structures> by sending each named element to its new interpretation; literal inclusion requires fixing the interpretations of those names.
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