Re: Goedel's Incompleteness Theorem and omega-consistency

Scott wrote:
Z(n) appears to presume that to any natural number n,
a closed term Z(n) can be assigned.

This is not merely a presumption. They in fact do have a
demonstrably constructible specific closed term in mind.
Z(n) is s(s(s(...(s(0)))), with n s's, as Rupert just said.

If [Neg (v Gen a)] belonged to Flg(c) for some class-sign a,
then couldn't we just add a new constant symbol 'x' to the theory as an
instance of such a counterexample, falsifying the first half of the
condition for omega-inconsistency?

I can't identify any "halves" in your quotation of the definition.
What piece specifically is this falsifying?
Write out the whole definition AGAIN and HIGHLIGHT the PART of it
that this is falsifying.
.