On 16 Jun., 21:40, MoeBlee <jazzm...@hotmail.com> wrote: > On Jun 16, 2:21 pm, MoeBlee <jazzm...@hotmail.com> wrote: > > > I don't have a thousand lifetimes to wait for you to show a > > formula P such that both P and ~P are derivable in ZFC from the above > > definition. > > CORRECTION: I should have said: > > [...] to show, for some formula P, a proof in ZFC (with said > definition included) of P and a proof in ZFC (with said definition > included)of ~P.
Look simply at the results. If a theory says that there is an uncountable set of real numbers such each number can be identified as a computable or definable or constructable one, or in other ways, then this theory is provably wrong. Reason: Cantor either proves that a countable set is uncountable or that a constructible/computable/definable number is not constructible/ computable/definable. What the theory internally may be able to prove or not to prove is, at least for my person, completely uninteresting.
