new version of equational formal systems manuscript

martdowd at martdowd at
Tue Mar 30 16:59:09 EDT 2021


I have a new version of
 "Equational Formal Systems for Arithmetic"
This corrects some errors in the old version, which I previously
posted a link to; the old link is no longer valid.

The new version has been expanded to include new results.  A list of
some of the results is as follows.
 - Various fundamental facts, including $(x-y)+y=(y-x)+x$, are shown
   to be provable in two particular weak systems.
 - The consistency of $\LA$ (polynomial time arithmetic) is provable
   in $\LE_2$A (double exponential arithmetic).
 - A polynomial time equation is provable in $\LE_2$A iff its bounded
   versions have polynomial length $\LA$ proofs, verifiably in $\LA$.
 - The consistency of ${\mathcal PS}\tA$ (polynomial space arithmetic)
   is provable in $\LE_2$A.
 - The consistency of ${\mathcal PS}\tA$
   follows in $\LA$ from the consistency of $\LA$.
 - $\cL_3$A (equivalent to elementary arithmetic) has two stratifications,
   one of which is provably strict.

Martin Dowd

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