Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures
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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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- last seen: 2026-05-19T01:45:01.086888+00:00