闭有序微分域中维数的符合

Pub Date : 2020-02-28 DOI:10.1215/00294527-2021-0013

Pantelis E. Eleftheriou, O. Sánchez, N. Regnault

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引用次数: 1

摘要

设$(R， \delta)$是一个闭有序微分域，$C$是一个常数域。在本文中，我们证明了在$(R, C)$对中可定义的集合，$\ -维与大维重合。作为一个应用，我们将$C$内部的可定义集合表征为在$(R, C)$中可定义且具有$\ δ $-维数$0$的集合。我们进一步表明，具有$\delta$-维度$0$通常并不意味着在$C$中具有共分析性。

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On Coincidence of Dimensions in Closed Ordered Differential Fields

Let $(R, \delta)$ be a closed ordered differential field, and $C$ its field of constants. In this note, we prove that for sets definable in the pair $(R, C)$, the $\delta$-dimension and the large dimension coincide. As an application, we characterize the definable sets that are internal to $C$, as those sets that are definable in $(R, C)$ and have $\delta$-dimension $0$. We further show that having $\delta$-dimension $0$ does not generally imply co-analyzability in $C$.

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