May 2021 On Coincidence of Dimensions in Closed Ordered Differential Fields
Pantelis E. Eleftheriou, Omar León Sánchez, Nathalie Regnault
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Notre Dame J. Formal Logic 62(2): 257-268 (May 2021). DOI: 10.1215/00294527-2021-0013


Let K=R,δ be a closed ordered differential field, in the sense of Singer, and let C be its field of constants. In this note, we prove that, for sets definable in the pair M=R,C, the δ-dimension of Brihaye, Michaux, and Rivière and the large dimension from of Eleftheriou, Günaydin, and Hieronymi coincide. As an application, we characterize the definable sets in K that are internal to C as those sets that are definable in M and have δ-dimension 0. We further show that, for sets definable in K, having δ-dimension 0 does not generally imply co-analyzability in C (in contrast to the case of transseries). We also point out that the coincidence of dimensions also holds in the context of differentially closed fields and in the context of transseries.


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Pantelis E. Eleftheriou. Omar León Sánchez. Nathalie Regnault. "On Coincidence of Dimensions in Closed Ordered Differential Fields." Notre Dame J. Formal Logic 62 (2) 257 - 268, May 2021.


Received: 27 February 2020; Accepted: 15 October 2020; Published: May 2021
First available in Project Euclid: 9 June 2021

Digital Object Identifier: 10.1215/00294527-2021-0013

Primary: 03C98
Secondary: 03C60 , 03C64

Keywords: closed ordered differential fields , dense pairs in o-minimal structures , differential dimension , large dimension

Rights: Copyright © 2021 University of Notre Dame


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Vol.62 • No. 2 • May 2021
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