Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.

中文翻译：

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O型痕迹具有很强的细胞分解特性

在有序基团的非评估弱o最小展开中，已证明了强大的细胞分解特性。在此注释中，我们表明所有o最小迹线都具有很强的细胞分解特性。同样在引入任意o最小结构中的非理性非评价割的概念之后，我们表明，非理性非评价割对o最小结构的每次扩展都是o最小迹线。