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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2503.09425 |
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| _version_ | 1866909657870630912 |
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| author | Guénet, Rémi |
| author_facet | Guénet, Rémi |
| contents | In arXiv:1303.3724, the authors provide an axiomatic way of constructing new polynomially bounded o-minimal structures. However, all of the structures satisfying these axioms must also have smooth cell-decomposition. In this paper, we generalize their approach by allowing weakly smooth germs into the construction. In particular, we showed in arXiv:2501.17583 that the o-minimal structure constructed in [O. Le Gal, J.-P. Rolin. "An o-minimal structure which does not admit $C^\infty$ cellular decomposition" Ann. Inst. Fourier 59 (2009), pp 543-562] satisfies the assumptions of our theorem. As an application of our result, we show that there exists an o-minimal structure within which we can define a nowhere smooth function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09425 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasianalytic algebras with weakly smooth germs generate o-minimal structures Guénet, Rémi Logic In arXiv:1303.3724, the authors provide an axiomatic way of constructing new polynomially bounded o-minimal structures. However, all of the structures satisfying these axioms must also have smooth cell-decomposition. In this paper, we generalize their approach by allowing weakly smooth germs into the construction. In particular, we showed in arXiv:2501.17583 that the o-minimal structure constructed in [O. Le Gal, J.-P. Rolin. "An o-minimal structure which does not admit $C^\infty$ cellular decomposition" Ann. Inst. Fourier 59 (2009), pp 543-562] satisfies the assumptions of our theorem. As an application of our result, we show that there exists an o-minimal structure within which we can define a nowhere smooth function. |
| title | Quasianalytic algebras with weakly smooth germs generate o-minimal structures |
| topic | Logic |
| url | https://arxiv.org/abs/2503.09425 |