On the arithmetization of real fields with exponentiation


Shepherdson proved that a discrete unitary commutative semi-ring A satisfies IE0 (induction scheme restricted to quantifier free formulas) iff A 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 and fields. Let T range over axiom systems for ordered fields… (More)