  We develop some basic results about full amalgamation classes with intrinsic
trascendentals. These classes have generics whose models may have finite
subsets whose intrinsic closure is not contained in its algebraic closure. We
will show that under fairly natural conditions the generic will have an
essentially undecidable theory, but we will also exhibit strictly superstable
and strictly simple examples. Separating types over a model into those that are
intrinsic and those that are extrinsic, we will demonstrate that the complexity
exceeding that of a simple theory in the classes with essentially undecidable
theories of [1] comes from the intrinsic types by deriving a class from them
which has a strictly simple theory with few intrinsic types.
  1. J. Brody and M.C. Laskowski, "On Rational Limits of Shelah-Spencer
Graphs", Journal of Symbolic Logic 77 (2012), no. 2, 580-592
