The combinatorics of tau-covers
  We solve four out of the six open problems concerning critical cardinalities of topological diagonalization properties involving tau-covers, show that the remaining two cardinals are equal, and give a consistency result concerning this remaining cardinal. Consequently, 21 open problems concerning potential implications between these properties are settled. We also give structural results based on the combinatorial techniques. 
Heike Mildenberger, Saharon Shelah, and Boaz Tsaban