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Mathematics Subject Classification: 11U09, 12H05, 12H10, 03C45, 03C60.
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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
http://dx.doi.org/10.15517/rmta.v26i2.33639
Artículo
Definable groups in DCFA
Grupos definibles en DCFA
1Universidad de Costa Rica, Centro de Investigación en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica. ronald.bustamante@ucr.ac.cr
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.
Acknowledgements
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
This is an open-access article distributed under the terms of the Creative Commons Attribution License
