Research Article
Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures
https://doi.org/10.21203/rs.3.rs-2773738/v1
This work is licensed under a CC BY 4.0 License
published 15 Feb, 2024
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Let R be a polynomially bounded o-minimal expansion of the realfield. Let f(z) be a transcendental entire function of finite order ρ and type σ∈[0, ∞]. The main purpose of this paper is to show that if (ρ<1) or (ρ=1 and σ=0), the restriction of f(z) on the real axis is not definable in R. Furthermore, we give a generalization of this result for any ρ∈[0,∞).
No competing interests reported.
published 15 Feb, 2024
Read the published version in Archive for Mathematical Logic →
Editorial decision: Revision requested
07 Nov, 2023
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First submitted to journal
03 Apr, 2023
You are reading this latest preprint version