Mathematics > Logic
[Submitted on 25 Jul 2016 (v1), last revised 24 Jan 2017 (this version, v2)]
Title:Dimension in the realm of transseries
View PDFAbstract:Let $\mathbb T$ be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of ${\mathbb T}^n$, also in relation to its codimension in the ambient space ${\mathbb T}^n$. The case of dimension $0$ is of special interest, and can be characterized both in topological terms (discreteness) and in terms of the Herwig-Hrushovski-Macpherson notion of co-analyzability. The proofs use results by the authors from "Asymptotic Differential Algebra and Model Theory of Transseries", the axiomatic framework for "dimension" in [L. van den Dries, "Dimension of definable sets, algebraic boundedness and Henselian fields", Ann. Pure Appl. Logic 45 (1989), no. 2, 189-209], and facts about co-analyzability from [B. Herwig, E. Hrushovski, D. Macpherson, "Interpretable groups, stably embedded sets, and Vaughtian pairs", J. London Math. Soc. (2003) 68, no. 1, 1-11].
Submission history
From: Matthias Aschenbrenner [view email][v1] Mon, 25 Jul 2016 08:02:57 UTC (22 KB)
[v2] Tue, 24 Jan 2017 00:21:44 UTC (23 KB)
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