### Small--large subgroups of the reals

by Roslanowski and Shelah. [RoSh:1081]

We are interested in subgroups of the reals that are small in
one and large in another sense. We prove that, in ZFC, there
exists a non--meager Lebesgue null subgrooup of
R, while it is consistent there there is no
non--null meager subgroup of R .

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