Thorn independence in the field of real numbers with a small multiplicative group

@article{Berenstein2007ThornII,
  title={Thorn independence in the field of real numbers with a small multiplicative group},
  author={Alexander Berenstein and Clifton Ealy and Ayhan G{\"u}naydin},
  journal={Ann. Pure Appl. Logic},
  year={2007},
  volume={150},
  pages={1-18}
}
We characterize þ-independence in a variety of structures, focusing on the eld of real numbers expanded by predicate de ning a dense multiplicative subgroup, G, satisfying the Mann property and whose pth powers are of nite index in G. We also show such structures are super-rosy and eliminate imaginaries up to codes for small sets. 

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