Submission date: 25 July 2016

Abstract:

Let T be the differential field of transseries. We establish some basic properties of the dimension of a definable subset of T^n, also in relation to its codimension in the ambient space 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].

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Full text arXiv 1607.07173: pdf, ps.