Consider a countable transitive model of ZFC $\mathfrak{M}$.
Let $X$ in $\mathfrak{M}$ be some definable set.
Can we define the "type" $p$ of nondefinable elements of $\mathfrak{M}$$X$? (By type I mean the set of formulas satisfied by the nondefinable elements).
Is $p$ principal or not? (By principal I mean whether $p$ has a generator or not).