  For a given material, \emph{controllable deformations} are those deformations
that can be maintained in the absence of body forces and by applying only
boundary tractions. For a given class of materials, \emph{universal
deformations} are those deformations that are controllable for any material
within the class. In this paper, we characterize the universal deformations in
compressible isotropic implicit elasticity defined by solids whose constitutive
equations, in terms of the Cauchy stress $\boldsymbol{\sigma}$ and the left
Cauchy-Green strain $\mathbf{b}$, have the implicit form
$\boldsymbol{\mathsf{f}}(\boldsymbol{\sigma},\mathbf{b})=\mathbf{0}$. We prove
that universal deformations are homogeneous. However, an important observation
is that, unlike Cauchy (and Green) elasticity, not every homogeneous
deformation is permissible for a given implicit-elastic solid. In other words,
the set of universal deformations is material-dependent, yet it remains a
subset of homogeneous deformations.
