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arXiv · 2302.01609

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

Lothar Sebastian Krapp
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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, where the embedding is not necessarily elementary. This is a consequence of an unconditional model theoretic embeddability result that we obtain by applying K\H{o}nig's Lemma.

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BibTeXRIS

Lothar Sebastian Krapp. 2023-02-03. Embedding the prime model of real exponentiation into o-minimal exponential fields. https://doi.org/10.1112/blms.12972

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