[FOM] inductive definitions in first order logic

[Gergely Buday]

Dear FOMers,

in a recent paper of Denecker I have found the following:

"It is well-known that, in general, inductive definitions cannot be
expressed in first-order logic (FO)."

Could you please point me to the literature where this claim is
argumented? And, what does "in general" means? This suggests that in
special cases it is possible to include inductive definitions into
predicate logic.

Thanks

- Gergely