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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.26 n.2 San José Jul./Dec. 2019 


Definable groups in DCFA

Grupos definibles en DCFA

Ronald F. Bustamante-Medina1 

1Universidad de Costa Rica, Centro de Investigación en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.


E. Hrushovski proved that the theory of difference-differential fields of characteristic zero has a model-companion. We denote it DCFA. In this paper we study definable abelian groups in a model of DCFA. First we prove that such a group is embeddable on an algebraic group. Then, we study one-basedeness, stability and stable embeddability of abelian definable groups.

Keywords: model theory of fields; supersimple theories; difference-differential fields; definable goups; abelian groups


E. Hrushovski demostró que la teoría de cuerpos diferenciables de diferencia de característica cero tiene una modelo-compañera. La denotamos DCFA. En este artículo estudiamos los grupos abelianos en un modelo de DCFA. Primero demostramos que tales grupos son isomorfos a un subgrupo de un grupo algebraico. Posteriormente, estudiaremos las propiedades de ser monobasados, estables y establemente inmersibles de grupos definibles abelianos.

Palabras clave: teoría de modelos de cuerpos; teorías supersimples; cuerpos diferenciales de diferencia; grupos definibles; grupos abelianos.

Mathematics Subject Classification: 11U09, 12H05, 12H10, 03C45, 03C60.

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The author acknowledges support from the School of Mathematics and the Research Center of Pure and Applied Mathematics (CIMPA), project 821-B9-092, University of Costa Rica.


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Received: June 25, 2017; Revised: May 10, 2019; Accepted: May 23, 2019

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