SOME CARDINAL CHARACTERISTICS RELATED TO THE COVERING NUMBER AND THE UNIFORMITY OF THE MEAGRE IDEAL

We extend the concepts of splitting, reaping, and independent families to families of functions and permutations on omega and define associated cardinal characteristics s(f), s(p), r(f), r(p), i(f), and i(p). We study relationships among cov(M), non(M), and these cardinals. In this paper, we show that s(f) = non(M) = s(p), r(f) = cov(M) <= r(p), and cov(M) <= i(f), i(p).