English

Green points in the reals

Logic 2025-10-17 v2

Abstract

We construct an expansion of a real closed field by a multiplicative subgroup adapting Poizat's theory of green points. Its theory is strongly dependent, and every open set definable in a model of this theory is semialgebraic. We prove that the real field with a dense family of logarithmic spirals, proposed by Zilber, satisfies our theory.

Keywords

Cite

@article{arxiv.2501.01176,
  title  = {Green points in the reals},
  author = {Yilong Zhang},
  journal= {arXiv preprint arXiv:2501.01176},
  year   = {2025}
}
R2 v1 2026-06-28T20:54:29.044Z