Open Access
2011 Rank and Dimension in Difference-Differential Fields
Ronald F. Bustamante Medina
Notre Dame J. Formal Logic 52(4): 403-414 (2011). DOI: 10.1215/00294527-1499363


Hrushovski proved that the theory of difference-differential fields of characteristic zero has a model-companion, which we shall denote DCFA. Previously, the author proved that this theory is supersimple. In supersimple theories there is a notion of rank defined in analogy with Lascar U-rank for superstable theories. It is also possible to define a notion of dimension for types in DCFA based on transcendence degree of realization of the types. In this paper we compute the rank of a model of DCFA, give some properties regarding rank and dimension, and give an example of a definable set with finite rank but infinite dimension. Finally we prove that for the case of definable subgroup of the additive group being finite-dimensional and having finite rank are equivalent.


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Ronald F. Bustamante Medina. "Rank and Dimension in Difference-Differential Fields." Notre Dame J. Formal Logic 52 (4) 403 - 414, 2011.


Published: 2011
First available in Project Euclid: 4 November 2011

zbMATH: 1247.03051
MathSciNet: MR2855879
Digital Object Identifier: 10.1215/00294527-1499363

Primary: 11U09 , 12H05 , 12H10

Keywords: definable sets , difference-differential fields , model theory of fields , supersimple theories

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 4 • 2011
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