We study groups definable in tame expansions of -stable theories. Assuming several tameness conditions, we obtain structural theorems for groups definable and interpretable in these expansions. As our main example, by characterizing independence in the pair , where is an algebraically closed field and is a multiplicative subgroup of with the Mann property, we show that the pair satisfies the assumptions. In particular, this provides a characterization of definable and interpretable groups in in terms of algebraic groups in and interpretable groups in . Furthermore, we compute the Morley rank and the -rank in and both ranks agree.
Notre Dame J. Formal Logic
60(2):
161-194
(May 2019).
DOI: 10.1215/00294527-2019-0003
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