= Universal sentence
{title2=$\forall\mathbf x\,\psi(\mathbf x)$}
A <universal sentence> has the form $\forall\mathbf x\,\psi(\mathbf x)$ with <quantifier-free formula> $\psi$, including an empty quantifier block. Its truth passes from a <first-order structure> to every <substructure of a first-order structure>: tuples from the smaller domain are also tuples of the larger domain, and quantifier-free truth agrees. Therefore a <first-order theory> of <universal sentences> has a <first-order model> class closed under <substructures of a first-order structure>.
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