Abstract
Let \({\mathcal {R}}\) be a polynomially bounded o-minimal expansion of the real field. Let f(z) be a transcendental entire function of finite order \(\rho \) and type \(\sigma \in [0,\infty ]\). The main purpose of this paper is to show that if (\(\rho <1\)) or (\(\rho =1\) and \(\sigma =0\)), the restriction of f(z) to the real axis is not definable in \({\mathcal {R}}\). Furthermore, we give a generalization of this result for any \(\rho \in [0,\infty )\).
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Sfouli, H.: Some nondefinability results with entire functions in a polynomially bounded o-minimal structure. Arch. Math. Logic 59, 733–741 (2020)
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Hassan Sfouli wrote the main manuscript.
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Sfouli, H. Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures. Arch. Math. Logic 63, 491–498 (2024). https://doi.org/10.1007/s00153-024-00904-x
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DOI: https://doi.org/10.1007/s00153-024-00904-x