Algebraically prime extension test for quantifier elimination
= Algebraically prime extension test for quantifier elimination
= QET2
{c}
{synonym}
If $T$ has <algebraically prime models> and every inclusion between models of $T$ is a <simple closure>, then $T$ has <quantifier elimination>. For a common base $A$, embed its algebraically prime extension into both models. Simple closure transfers a witness into that extension; the second embedding transfers it to the other model.