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Definable Additive Subgroups of Partial Differential Fields of Characteristic Zero with an Automorphism

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Bustamante Medina, Ronald F.

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Abstract

Abstract.The theory of partial differential fields of characteristic zero withan automorphism has a model companion denoted DCFmA. This theory isnot complete, but its completions are easily discribed. They are supersimpleand eliminate imaginaries. In this paper we prove that the definable subgroupsif the additive group of a model of DCFmA are not 1-based and we study theprolongations and arc spaces of the diagonal subgroups.

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model theory of fields, supersimple theories, difference-differential fields, definable groups, abelian groups

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