Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Algebraic jet spaces and Zilber’s dichotomy in DCFA
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Keywords

Model Theory of Fields
Supersimple Theories
Difference-Differential Fields
Definable Sets
Teoría de modelos
teorías supersimples
campos diferenciales de diferencia
conjuntos definibles

How to Cite

Bustamante Medina, R. F. (2010). Algebraic jet spaces and Zilber’s dichotomy in DCFA. Revista De Matemática: Teoría Y Aplicaciones, 17(1), 1–12. https://doi.org/10.15517/rmta.v17i1.308

Abstract

This is the first of two papers devoted to the proof of Zilber’s dichotomy for the case of difference-differential fields of characteristic zero. In this paper we use the techniques exposed in [9] to prove a weaker version of the dichotomy, more precisely, we prove the following: in DCFA the canonical base of a finite-dimensional type is internal to the fixed field of the field of constants. This will imply a weak version of Zilber’s dichotomy: a finite-dimensional type of SU -rank 1 is either 1-based or non-orthogonal to the fixed field of the field of constants.

https://doi.org/10.15517/rmta.v17i1.308
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References

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