Let $M$ be a first order structure. Let $A$ and $B$ be sets of parameters from $M$ . Let $p$ be a complete $n$ -type over $B$ . Then we say that $p$ is an $A$ -definable type iff for every formula $\psi(\bar{x},\bar{y})$ with ln$(\bar{x})=n$ , there is some formula $d\psi(\bar{y},\bar{z})$ and some parameters $\bar{a}$ from $A$ so that for any $\bar{b}$ from $B$ we have $\psi(\bar{x},\bar{b}) \in p$ iff $M \models d\psi(\bar{b},\bar{a})$ .

Note that if $p$ is a type over the model $M$ then this condition is equivalent to showing that $\{\bar{b} \in M:\psi(\bar{x},\bar{b}) \in M\}$ is an $A$ -definable set.

For $p$ a type over $B$ , we say $p$ is definable if it is $B$ -definable.

If $p$ is definable, we call $d\psi$ the defining formula for $\psi$ , and the function $\psi \mapsto d\psi$ a defining scheme for $p$ .