Avoiding equal distances

@article{Kumar2017AvoidingED,
  title={Avoiding equal distances},
  author={Ashutosh Kumar and Saharon Shelah},
  journal={Fundamenta Mathematicae},
  year={2017},
  volume={236},
  pages={263-267}
}
We show that it is consistent that there is a non meager set of reals each of whose non meager subsets contains equal distances. 
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