Assume
β
\beta
is weakly admissible over
0
0
and
0
1
/
2
{0^{1\,/\,2}}
. It follows that the
β
\beta
-recursively enumerable degrees are dense. In addition each
β
\beta
-recursively enumerable degree above
0
1
/
2
{0^{1\,/\,2}}
is the half-jump of some tamely
β
\beta
-recursively enumerable degree below
0
1
/
2
{0^{1\,/\,2}}
.