David Corfield Shelah's main gap

A countable first order theory falls in one of the two classes:

• (intractable:) has the maximal number of models in all sufficiently large cardinalities

• every model can be decomposed as a tree of countable models

There are some generalizations of this dichotomy beyond first order theories.

• L. Harrington, M. Makkai, An exposition of Shelah’s “in gap’’: counting uncountable models of ∞-stable and superstable theories, Notre Dame J. Formal Logic 26 (1985), no. 2, 139–177 doi euclid