The consistency of peano arithmetic: a defeasible perspective

This paper proposes to replace PA, Peano Arithmetic, by a theory APA defined in terms of (i) a set of axioms that is classically equivalent to the Peano axioms and (ii) a defeasible logic that minimizes inconsistency, viz.\ an inconsistency-adaptive logic. If PA is consistent, its set of theorems coincides with the set of APA-theorems. If PA is inconsistent, APA is non-trivial and has the following remarkable property: there is a unique non-standard number that is its own successor and every `desirable' PA-theorem is retained if restricted to the other numbers. The restriction can be expressed in the language of arithmetic. And there is much more