unprovability of consistency of a smaller theory

[martdowd at aol.com]

FOM:

In the paper linked to in
 https://cs.nyu.edu/pipermail/fom/2020-February/021995.html
I showed that the consistency of polynomial time arithmetic is provable
in double exponential time arithmetic, and left open the question of
whether it is provable in single exponential time arithmetic.

Proving that this is not the case would be an example of proving
that the consistency of a theory T1 was not provable in a stronger
theory T2.

Examples of such theorems in the literature include:

J. Paris and A. Wilkie.  On the scheme of induction for bounded
arithmetic formulas.  Annals of Pure and Applied Logic, 35:261­302, 1987.
Here it is shown that the consistecy of Robinson's Q is not provable in
in I-Delta_0+exp (elementary arithmetic).

Samuel R. Buss and Aleksandar Ignjatovic.  Unprovability of consistency
statements in fragments of bounded arithmetic.                                  
Annals of Pure and Applied Logic, 74:221­244, 1995.                             
Among the results of this, it is shown that the consistency
of PV minus induction is not provable in PV.

If anyone knows of other relevant papers please post references
on this thread.

Thanks,
Martin Dowd

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