Assume rotation is relative.  This causes three paradoxes:

1. From the perspective of a non-universal rotating body, the rest of the
universe looks as if it's rotating *around* it.  If rotation is relative,
this must be true from the perspective of the bodt.  This clearly violates
the laws of motiom and acceleration (even from the perspective of the body),
independently of any axioms about the relativity of rotation per se, because
centrifugal force would immediately start pulling the universe apart.
Centrifugal force itself can be viewed merely as the natural progression of
motion along a straight line due to inertia.

2. If rotation were given its behaviour by relation to an absolute rotation
(or lack of rotation) of the entire universe, then an object rotating
relative to the universe, away from the universe's center, would fly away
from the universe's center because, relative to its rotation, the rest of
the universe is rotating about its center.

3. If rotation is relative to the whole universe, this implies an axis, or
center of rotation (or non-rotation, as the universe's rotation relative to
itself would be null), for the universe.  Although the universe is not
rotating, measuring non-universal objects' rotation against the rotational
velocity (0) of the universe implies that another non-universal rotational
velocity could have acted as 0 instead, for example such as to make what
would otherwise be rotating, not rotating, in which case the two hypothetical
rotational velocities of the universe, which are required by principle, have
a rotational difference, and that requires a specific center of rotational
difference.  Therefore, a concept of rotational velocity being relative to
the universe requires a specific center of the universe.  Yet, under this
theory, *where the center is* can have no effect on physics or its
application (and thus cannot be detected) (and if it did, then 2. would
apply), so we're required to have ghost information; a placeholder for
nothing.  

Therefore, we can determine, a priori, that rotation cannot be relative.
Therefore, we don't need Mach's principle to explain rotational velocity, and
since it makes rotational velocity out to be relative to that of the mass of
of the entire universe (and not to mention that it answers an invalid
question), Mach's principle must be false.