You missed the point. Any "bad" Godel's number can be interpreted as "good" Lisivka's number. We have ambiguity here, because a number can refer to any formula in infinite number of sets.
> We can go further. We can even construct PM-Lisp formulas in PM-Lisp!
No, we cannot.
When you say "You missed the point.", and "No, we cannot" -- your words come off as though you are supremely confident, and a bit condescending. This makes me not want to engage deeper with you.
To see how it feels:
No, drran, you have missed the point. Read it again, maybe you'll get it.
4667698044567788679899973453457778678980909855464564564578787890665467786780909875744564756867978980890785745635646767586445454536665474747746767457575890112345678999077554344567787923424234234234246566797899707980980983453453454353453453453534534534534
This number is equivalent to the proof that I'm right. Godel was genius!
Try going through the essay, and point out where the “incorrect” numbers were formed. You may be surprised to find that all statements were “correct” in the definition you are thinking of. The mathematical term is “primitive recursive” and “well-formed”