Re: A simple paradox in Godels incompleteness theorem that invalidat

On Oct 14, 11:36 am, Peter_Smith <ps...@xxxxxxxxx> wrote:
On 14 Oct, 19:12, Newberry <newberr...@xxxxxxxxx> wrote:

The question was if a proof existed that all conceivable theories that
represent all p.r. functions must necessarily be omega-incomplete. If
you look at Goedel's paper he only claims that all such theories must
be syntactically incomplete. His Theorem VI is about syntactical
incompleteness.

But he proves incompleteness for theories satisfying certain
conditions precisely by giving an example of the omega-incompleteness
of such theories (i.e. telling us how to construct an unprovable
sentence AxFx each of whose instances are provable).

Could a theory satisfying those conditions be (syntactically)
incomplete for a different reason than PM?

.