Re: Metamathematically True or False?


Torkel Franzen wrote:
> "Charlie-Boo" <chvol@xxxxxxx> writes:
>
> > I wonder if there is an additional simple condition on the wff
> > that ensures the above i.e. "If a wff passes such-and-such a
> > condition, then the set expressed is r.e. iff the set expressed is the
> > set represented."?
>
> Sure, Sigma_1-formulas, assuming T to be Sigma-sound (1-consistent).
> Again I recommend Smullyan's book.

Isn't the set expressed by a Sigma-1 formula always r.e.? Whereas it
would be the case that the set expressed by a Sigma-1 formula is always
the set represented only if T were Sigma-1-complete.

.

Relevant Pages

  • Re: Metamathematically True or False?
    ... > I wonder if there is an additional simple condition on the wff ... then the set expressed is r.e. iff the set expressed is the ... Again I recommend Smullyan's book. ... Prev by Date: ...
    (sci.logic)
  • Re: Metamathematically True or False?
    ... Rupert wrote: ... > Isn't the set expressed by a Sigma-1 formula always r.e.? ... RELEVANT sense here! ... Prev by Date: ...
    (sci.logic)