Mathias forcing and combinatorial covering properties of filters
  We give topological characterizations of filters $F$ on $w$ such that the Mathias forcing $M_F$ adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzm\'an, Hru\v{s}\'ak, Mart\'{\i}nez, Minami, and Tsaban. 
David Chodounsk\'y, Du\v{s}an Repov\v{s}, Lyubomyr Zdomskyy
math.LO math.GN