Rank and dimension in difference-differential fields
type: Item
instance of: scholarly article
title: Rank and dimension in difference-differential fields
zbMATH Open document ID: 1247.03051
DOI: 10.1215/00294527-1499363
author: Ronald F. Bustamante Medina
published in: Notre Dame Journal of Formal Logic
publication date: 2011-12-21T00:00:00Z
review text: The model companion DCFA of the theory of difference-differential fields of characteristic 0 is considered. It is known that the completions of DCFA are supersimple. The author computes their SU-rank and compares it and a notion of dimension based on the transcendence degree of realizations of types. In particular, an example of a definable set with SU-rank 1 but infinite dimension is provided. On the other hand it is shown that a definable subgroup of the additive group is finite-dimensional if and only if it has finite SU-rank.
reviewed by: Carlo Toffalori
Mathematics Subject Classification ID: 03C45
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 12H10
Mathematics Subject Classification ID: 12L12
zbMATH DE Number: 5991007
zbMATH Keywords: difference-differential field
zbMATH Keywords: supersimple theory
zbMATH Keywords: SU-rank
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/00294527-1499363
OpenAlex ID: W1977676985
description: scientific article; zbMATH DE number 5991007