categoricity

In model theory, given a cardinal $\kappa $, a theory is **$\kappa $-categorical** (or categorical in cardinality $\kappa $), if it has precisely one isomorphism class of models of cardinality $\kappa $. The **Morley categoricity theorem** says that a first-order theory $T$ with countably many symbols is $\kappa $-categorical for one uncountable cardinal $\kappa $ iff $T$ is categorical in any uncountable cardinality.

- John Baldwin,
*Categoricity*, Amer. Math. Soc. 2011, pdf - John T. Baldwin,
*What is a complete theory*, talk, pdf - wikipedia: Morley categoricity theorem

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

Created on June 9, 2012 18:34:25
by Zoran Škoda
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