One of the ways to define the Morley rank of a definable set is with respect to a model, say $M$, i.e. a set has rank $\alpha+1$ if there are infinitely many definable subsets with parameters in $M$ of rank $\alpha$ (and a similar clause for limit ordinals). One then shows that once $M$ is $\aleph\_0$-saturated then considering definable subsets with parameters in elementary extensions of $M$ doesn't change the rank.


However, in some theories, e.g. algebraically closed fields of fixed characteristic, any model will do, i.e. Cantor-Bendxson rank and Morley rank coincide.


What is known about this phenomenon, i.e. in which theories Cantor-Bendixson equals Morley rank in any (not necessary $\aleph\_0$-saturated) model?



computing Morley rank using parameters from an arbitrary model
The distinction between Morley rank as defined by arbitrary formulas and by definable families of formulas is essential. $\aleph\_1$- categoricity in particular implies the rank can defined by
definable families. Since my 1973 [?] article in the transactions AMS or Shelah's book or 
say Pillay's geometric model theory book


