| Abstract: | A subset A of a Boolean algebra B is said to be (n,m)-reapedif there is a partition of unity p  B of size n such that |{b p:b  a  0}|  m for all a A. The reaping number rn,m (B) ofa Boolean algebra B is the minimum cardinality of a set A B\{0}which cannot be (n,m)-reaped. It is shown that for each n , thereis a Boolean algebra B such that rn+1,2(B) rn,2(B). Also, {rn,m(B):m n } consists of at most two consecutive cardinals. The existenceof a Boolean algebra B such that rn,m (B) rn',m' (B) is equivalentto a statement in finite combinatorics which is also discussed. |
