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.
"Tame Expansions of -Stable Theories and Definable Groups." Notre Dame J. Formal Logic 60 (2) 161 - 194, May 2019. https://doi.org/10.1215/00294527-2019-0003