English

A quasianalytic class with weakly smooth germs

Logic 2025-02-28 v2

Abstract

In [O. Le Gal, J.-P. Rolin. An o-minimal structure which does not admit CC^\infty cellular decomposition. In: Ann. Inst. Fourier 59 (2009), pp 543-562], the authors construct an o-minimal structure which does not admit smooth cell-decomposition. We explain in an appendix that their proof of o-minimality is incomplete and we give a complete proof in the main text.

Cite

@article{arxiv.2501.17583,
  title  = {A quasianalytic class with weakly smooth germs},
  author = {R. Guénet},
  journal= {arXiv preprint arXiv:2501.17583},
  year   = {2025}
}

Comments

36 pages; changed the height of admissible trees to be an ordinal instead of an integer in Definition 3.4

R2 v1 2026-06-28T21:23:39.015Z