Existential theory of a structure
= Existential theory of a structure
{title2=$\operatorname{Th}_\exists(A)$}
The <existential theory of a structure> is the <set> of <existential sentences> with quantifier-free matrices true in it. Its witnesses persist in extensions because quantifier-free truth is preserved by <structure embeddings>. It differs from an existential diagram, which additionally uses names for <Elements>.