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Science Forum Index » Logic Forum » Theories that prove their own consistency...
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| Gc... |
 Posted: Thu May 15, 2008 1:15 pm |
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Guest
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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? |
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| abo... |
| Posted: Thu May 15, 2008 7:10 pm |
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Guest
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On May 16, 1:15 am, Gc <Gcut... at (no spam) hotmail.com> wrote:
Quote: 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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