[FOM] Is PA + ~Con(PA) a complete theory?

Aatu Koskensilta Aatu.Koskensilta at uta.fi
Wed Jun 5 01:49:08 EDT 2013

Quoting Andrew Polonsky <andrew.polonsky at gmail.com>:

> Let T be the theory obtained by adding to PA the axiom
> Incon(PA) = exists n. n is a code of a PA-derivation of Falsum
> Since T is a consistent c.e. theory extending PA, one would expect to have
> undecidable propositions in it.  Are there any known examples of such
> propositions?

   Just take the Rosser sentence for PA + Incon(PA).

Aatu Koskensilta (aatu.koskensilta at uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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