Submission date: 3 February 2023.

Abstract:

Motivated 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. This is deduced from a more general unconditional result on the embeddability of exponential algebraic closures in o-minimal exponential fields.

Mathematics Subject Classification: 03C64 (03C60 12J15 12L12 12J10)

Keywords and phrases:

Full text arXiv 2302.01609: pdf, ps.