Arithmetization of the field of reals with exponentiation extended abstract
Shepherdson proved that a discrete unitary commutative semi-ring satisfies (induction scheme restricted to quantifier free formulas) iff is integral part of a real closed field; and Berarducci asked about extensions of this criterion when exponentiation is added to the language of rings. Let range over axiom systems for ordered fields with exponentiation; for three values of we provide a theory in the language of rings plus exponentiation...