Re: completeness what is it exactly

On Jul 9, 10:50 am, translogi <wilem...@xxxxxxxxxxxxxx> wrote:

.so i guess
A theory T is complete :<=> forall "A" (T |- A v T |- ~A)

 is false

if a is an variable/ contingent neither T |- A nor  T |- ~A

Do you mean where A is a formula that may have free variables in it?

If so, then, yes, "T is negation complete" does not say that for every
formula (even if it has free variables) A in the language of T, we
have T |- A or T |- ~A.

Rather, "T is negation complete" says that for every SENTENCE A in the
language of T, we have T |- A or T |- ~A.

MoeBlee
.