The best you can do is this:

  If P(0) and Pn -> P(n+1) *and* P(oo) then An in N* Pn.

But that's a god-awful hack made by adding the condition that P holds of
oo.  It's not a proper inductive principle at all (that is, it is not
induction because N* is not an initial algebra).

Say, you were telling me yesterday that Cantor's theorem is invalid.
Let's discuss that.  Show me the invalid step already, will you?

--
"And God Himself won't help you if this goes bad as despite your
beliefs I can assure you that angry people will against all law if
necessary tear their rage out of your hides if it goes badly."
  -- James S. Harris, on the dangers of criticizing his mathematics