nLab
categoricity

Contepts

Idea

In model theory, given a cardinal κ\kappa, a theory is κ\kappa-categorical (or categorical in cardinality κ\kappa), if it has precisely one isomorphism class of models of cardinality κ\kappa.

Properties

The Morley categoricity theorem says that a first-order theory TT with countably many symbols is κ\kappa-categorical for one uncountable cardinal κ\kappa iff TT is categorical in any uncountable cardinality.

Study of categoricity lead historically to the development of the stability theory in model theory, see also geometric stability theory.

References

Revised on January 4, 2015 08:37:43 by Urs Schreiber (127.0.0.1)