Combinatorics for the Dominating and Unsplitting Numbers
by
Jason Aubrey
University of Michigan

It is known that cf(d) is at least as large as b, and thanks to Mildenberger and Blass it is also known to be at least as large as g, and s. Furthermore, it is known that that if one partitions a dominating family into < b pieces, then one of pieces is actually dominating (not just of cardinality d), and if one partitions a dominating family into < g pieces, then (again thanks to Mildenberger and Blass) one of the pieces is 2-dominating. I will give a similar characterization for partitions of dominating families into < s pieces, and apply this characterization to obtain results on the unsplittting and sigma-unsplitting numbers.

Date received: March 21, 2002