Abstract: We define the class of thick cats
(compact abstract theories, which contains in
particular semi-Hausdorff, Hausdorff and first order cats), and
prove that in this class simplicity behaves as in first
order theories.
We consider well-known first order notions, such as
interpretability or stable dividing/reduct, and propose analogous
notions that can be naturally expressed in terms of maps between
type-space functors.
We prove several desirable properties of the new notions and show
the connection between them and their classical
counterparts.
We conclude with several scattered results concerning cats and
simplicity.
Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue, Room 2-101 Cambridge, MA 02139-4307 U.S.A.
, http://www-math.mit.edu/~pezz
