preprint · Research Square
Abstract 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,∞).
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DOI: 10.21203/rs.3.rs-2773738/v1
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