  In the BCSS model of real number computations we prove a concrete and
explicit semi-decidable language to be undecidable yet not reducible from (and
thus strictly easier than) the real Halting Language. This solution to Post's
Problem over the reals significantly differs from its classical, discrete
variant where advanced diagonalization techniques are only known to yield the
existence of such intermediate Turing degrees. Strengthening the above result,
we construct (that is, obtain again explicitly) as well an uncountable number
of incomparable semi-decidable Turing degrees below the real Halting problem in
the BCSS model. Finally we show the same to hold for the linear BCSS model,
that is over (R,+,-,<) rather than (R,+,-,*,/,<).
