Shelah’s main gap is a result in stability theory (part of model theory), which seeks to identify those first-order theories whose models admit some sort of reasonable classification. The ‘main gap’ describes a fundamental dichotomy between theories.
Roughly speaking, a countable first-order theory belongs to 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.
Last revised on May 20, 2015 at 08:30:26. See the history of this page for a list of all contributions to it.