Embedding the prime model of real exponentiation into o‐minimal exponential fields

Abstract

AbstractMotivated by the decidability question for the theory of real exponentiation and by the Transfer Conjecture for o‐minimal exponential fields, we show that, under the assumption of Schanuel's Conjecture, the prime model of real exponentiation is embeddable into any o‐minimal exponential field, where the embedding is not necessarily elementary. This is a consequence of an unconditional model theoretic embeddability result that we obtain by applying Kőnig's Lemma.