Universal-existential sentence
= Universal-existential sentence
{title2=$\forall\mathbf x\,\exists\mathbf y\,\theta(\mathbf x,\mathbf y)$}
A universal-existential sentence has a universal block followed by an existential block and a <quantifier-free formula>. Such axioms are preserved under unions of chains of structures: the universally chosen tuple occurs in one stage, whose existential witnesses remain in the union. An <inductive first-order theory> has an axiomatization by these sentences.