Abstract

We investigate the cofinality of the partial order N κ of functions from a regular cardinal κ into the ideal N of Lebesgue measure zero subsets of R. We show that when add(N) = κ and the covering lemma holds with respect to an inner model of GCH, then cf(N κ ) = max {cf(κ κ ), cf([ cf(N)] κ )}. We also give an example to show that the covering assumption cannot be removed