Author: aboabo Date: May 15, 2008 22:10
On May 16, 1:15Â am, Gc hotmail.com> wrote:> Hi,
>
> I have an impression that certain first order theories where the
> recursive definition of integer multiplication  is weakened can prove
> their own consistency, so the diagonalization doesn`t go trough but
> the consistency predicate is formalizable. I would like to know more,
> references/ explanations anybody?
Dan Willard, "Self Verifying Axiom Systems, the Incompleteness Theorem
and the Tangibility Reflection Princible" , Journal of Symbolic Logic
66 (2001) pp. 536-596.
Dan Willard, "An Exploration of the Partial Respects in which an Axiom
System Recognizing Solely Addition as a Total Function Can Verify Its
Own Consistency", Journal of Symbolic Logic 70 (2005) pp. 1171-1209.
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