A-type over a structure
= A-type over a structure
{c}
{title2=$p(\bar x)\text{ over }A\subseteq M$}
For $A\subseteq M$, an A-type over <first-order structure> $M$ is a set of formulas in a fixed finite tuple of variables, with parameters in $A$, consistent with the complete theory of $M$ expanded by constants for $A$. Every finite subset is realized in $M$. A <complete type> decides all formulas in its variables over those parameters.