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

Created on May 19, 2015 at 06:21:24. See the history of this page for a list of all contributions to it.