Consider structures (ω,k,γ) where ω is an algebraically closed field of characteristic zero, k is a subfield, and γ is a subgroup of the multiplicative group of ω. Certain pairs (k,γ) have been singled out as Mann pairs in [4]. We give new examples of such Mann pairs, we axiomatize for each Mann pair (k,γ) the first-order theory of (ω,k,γ) in a cleaner way than in [4], and, as the main result of the article, we characterize the subsets of ωn that are definable in (ω,k,γ).
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