In a definition like the following:
An object $x$ is called $P$ if [and only if] it has properties $p$ and $q.$
should one use an implication (if) or an equivalence (if and only if)?
It makes sense to use an equivalence seen as this is a definition and not a set of necessary conditions. However, in many texts I see the use of just an implication. Which is correct in the formal or stylistic sense?
It is quite common to use if instead of iff in definitions because it reads better.
An alternative is to use when instead of if.
A definition like “$x$ is called a blip when $x$ satisfies $p$ and $q$” is metalanguage.
The mathematical statement “$x$ is a blip iff $x$ satisfies $p$ and $q$” is true, as consequence of the definition, but is not quite the same thing.