  In relativistic space-time, Bohmian theories can be formulated by introducing
a privileged foliation of space-time. The introduction of such a foliation - as
extra absolute space-time structure - would seem to imply a clear violation of
Lorentz invariance, and thus a conflict with fundamental relativity. Here, we
consider the possibility that, instead of positing it as extra structure, the
required foliation could be covariantly determined by the wave function. We
argue that this allows for the formulation of Bohmian theories that seem to
qualify as fundamentally Lorentz invariant. We conclude with some discussion of
whether or not they might also qualify as fundamentally relativistic.
