Abstract

BUSTAMANTE-MEDINA, Ronald F.. Definable groups in DCFA. Rev. Mat [online]. 2019, vol.26, n.2, pp.179-195. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v26i2.33639.

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.

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