  We have recently proposed a special class of scalar tensor theories known as
the Fab Four. These arose from attempts to analyse the cosmological constant
problem within the context of Horndeski's most general scalar tensor theory.
The Fab Four together give rise to a model of self-tuning, with the relevant
solutions evading Weinberg's no-go theorem by relaxing the condition of
Poincare invariance in the scalar sector. The Fab Four are made up of four
geometric terms in the action with each term containing a free potential
function of the scalar field. In this paper we rigorously derive this model
from the general model of Horndeski, proving that the Fab Four represents the
only classical scalar tensor theory of this type that has any hope of tackling
the cosmological constant problem. We present the full equations of motion for
this theory, and give an heuristic argument to suggest that one might be able
to keep radiative corrections under control. We also give the Fab Four in terms
of the potentials presented in Deffayet et al's version of Horndeski.
