Several comments about the combinatorics of tau-covers

In a previous work with Mildenberger and Shelah, we showed that the combinatorics of the selection hypotheses involving tau-covers is sensitive to the selection operator used. We introduce a natural generalization of Scheepers' selection operators, and show that: (1) A slight change in the selection operator, which in classical cases makes no difference, leads to different properties when tau-covers are involved. (2) One of the newly introduced properties sheds some light on a problem of Scheepers concerning tau-covers. Improving an earlier result, we also show that no generalized Luzin set satisfies U_fin(Gamma,Tau).