The distinction between Morley rank as defined by arbitrary formulas and by definable familes 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

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