Inglés (pdf)
Articulo en XML
Referencias del artículo
Traducción automática
Enviar articulo por email
Permalink
Mathematics Subject Classification: 11U09, 12H05, 12H10, 03C45, 03C60.
Ver contenido complete en PDF
Servicios Personalizados
Revista
Articulo
Indicadores
-
Citado por SciELO -
Accesos
Links relacionados
-
Similares en
SciELO
Compartir
Revista de Matemática Teoría y Aplicaciones
versión impresa ISSN 1409-2433
Rev. Mat vol.26 no.2 San José jul./dic. 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.
References
R, Bustamante. Differentially closed fields of characteristic zero with a generic automorphism, Revista de Matemática: Teorı́a y Aplicaciones 14 (2007), no. 1, 81-100. [ Links ]
R, Bustamante. Algebraic jet spaces and Zilber’s dichotomy in DCFA, Revista de Matemática: Teorı́a y Aplicaciones 17 (2010), no. 1, 1-12. [ Links ]
R, Bustamante. Rank and dimension in difference-differential fields, Notre Dame Journal of Formal Logic 52 (2011), no. 4, 403-414. [ Links ]
R, Bustamante. Arc spaces and Zilber’s dichotomy in dcfa, submitted, 2019. [ Links ]
Z, Chatzidakis; E, Hrushovski. Model theory of difference fields, Trans. Amer. Math. Soc. 351 (1999), no. 8, 2997-3071. [ Links ]
Z, Chatzidakis; A, Pillay. Generic structures and simple theories, Ann. Pure Appl. Logic 95 (1998), no. 1-3, 71-92. [ Links ]
E, Hrushovski. Unidimensional theories are superstable, Ann. Pure Appl. Logic 50 (1990), no. 2, 117-137. [ Links ]
E, Hrushovski. The Manin-Mumford conjecture and the model theory of difference fields, Ann. Pure Appl. Logic 112 (2001), no. 1, 43-115. [ Links ]
P, Kowalski; A, Pillay. A note on groups definable in difference fields, Proc. Amer. Math. Soc. 130 (2001), no. 1, 205-212. [ Links ]
S, Lang. Abelian Varieties, reprint of the 1959 original, Springer, New York, 1983. [ Links ]
D, Marker. Manin kernels, Connections between model theory and algebraic and analytic geometry, Vol. 6, Dipartimento di Matematica della Seconda Univ. di Napoli, Caserta, 2000. [ Links ]
A, Pillay. Some foundational questions concerning differential algebraic groups, Pacific J. Math. 179 (1997), no. 1, 179-200. [ Links ]
A, Pillay. Definability and definable groups in simple theories, J. Symbolic Logic 63 (1998), no. 3, 788-796. [ Links ]
F,O, Wagner. Simple Theories, Kluwer Academic Publishers, Dordrecht, 2000. [ Links ]
F,O, Wagner . Some remarks on one-basedness, J. Symbolic Logic 69 (2004), no. 1, 34-38. [ Links ]
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
