Towards Trans-Exponential O-minimal Expansion of $(\mathbb{R},+,\cdot, 0, 1 <)$

Yayi Fu

Towards Trans-Exponential O-minimal Expansion of $(\mathbb{R},+,\cdot, 0, 1 <)$

Logic 2026-04-07 v1

Authors: Yayi Fu

Abstract

We add an analytic trans-exponential function $\varphi$ to $\mathbb{R}_{an,\exp}$ . We reduce the o-minimality of $\mathbb{R}_{an,\exp,\varphi}$ to the existence of "many" regular values for some definable systems of functions, which is a necessary condition for the o-minimality of $\mathbb{R}_{an,\exp,\varphi}$ .

Keywords

o-minimality trans-exponential function o-minimal expansion real numbers regular values definable systems

Cite

@article{arxiv.2604.03477,
  title  = {Towards Trans-Exponential O-minimal Expansion of $(\mathbb{R},+,\cdot, 0, 1 <)$},
  author = {Yayi Fu},
  journal= {arXiv preprint arXiv:2604.03477},
  year   = {2026}
}

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