  A representation embedding between cartesian theories can be defined to be a
functor between respective categories of models that preserves
finitely-generated projective models and that preserves and reflects certain
epimorphisms. This recalls standard definitions in the representation theory of
associative algebras. The main result of this paper is that a representation
embedding in the general sense preserves undecidability of theories. This
result is applied to obtain an affirmative resolution of a reformulation in
cartesian logic of a conjecture of M. Prest that every wild algebra over an
algebraically closed field has an undecidable theory of modules.
