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Theorem of Lion and o-minimal structures which do not admit $\mathcal {C}^{\infty }$-cell decompositions

Volume 124 / 2020

Zofia Rożen Annales Polonici Mathematici 124 (2020), 291-316 MSC: 03C64, 14P10. DOI: 10.4064/ap170626-30-9 Published online: 20 March 2020


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.


  • Zofia RożenInstitute of Mathematics
    Jagiellonian University
    30-348 Kraków, Poland

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