Some results on jumps of splittings of recursively enumerable sets

A recursively enumerable (r.e.) set A of degree $\underline a$ is said to have the universal jump splitting property (UJSP) if for each r.e. degree $\underline b$ below $\underline a$, there is a splitting of A into disjoint r.e. sets B and C such that $B\sp\prime$ has the same degree as $\underline b\sp\prime$. We show that there are r.e. sets A which fail to have UJSP. We also show that there is an r.e. set A such that the set of degrees of jumps of splittings of A is not dense in the degrees r.e. in $\emptyset\sp\prime$ and below $A\sp\prime$.