Recursive in A Generic Real

@article{Shinoda2000RecursiveIA,
  title={Recursive in A Generic Real},
  author={Juichi Shinoda and Theodore A. Slaman},
  journal={J. Symb. Log.},
  year={2000},
  volume={65},
  pages={164-172}
}
There is a comeager set C contained in the set of 1-generic reals and a first order structure M such that for any real number X, there is an element of C which is recursive in X if and only if there is a presentation of M which is recursive in X. 

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