Geodesic
On definable sets in some definably complete locally o-minimal structure
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1414-1425 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we show that the Grothendieck ring of a definably complete locally o-minimal expansion of the set (not the field) of real numbers $\mathbb R$ is trivial. Afterwards, we will give a sufficient condition for which a definably complete locally o-minimal expansion of an ordered group has no nontrivial definable subgroups. In the last section, we study some sets that are definable in a definably complete locally o-minimal expansion of an ordered field. Finally, a decomposition theorem for a definable set into finite union of $\pi_L$-quasi-special $\mathcal{C}^r$ submanifolds is demonstrated.
Keywords: Definably complete, locally o-minimal structures, Grothendieck rings. 
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M. Berraho. On definable sets in some definably complete locally o-minimal structure. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1414-1425. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a16/

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