Theorem of Lion and o-minimal structures which do not admit $\mathcal {C}^{\infty }$-cell decompositions
Volume 124 / 2020
Annales Polonici Mathematici 124 (2020), 291-316
MSC: 03C64, 14P10.
DOI: 10.4064/ap170626-30-9
Published online: 20 March 2020
Abstract
We use a theorem of Lion in order to give a rich family of examples of o-minimal structures which do not admit $\mathcal {C}^{\infty }$-cell decompositions. In particular we show the existence of fields $F_1$, $F_2$ such that each of them is the Hardy field of some o-minimal structure, they generate together a Hardy field containing $F_1(F_2)$, but that Hardy field cannot be the Hardy field of any o-minimal structure.
