PlanetMath: $\kappa$-categorical

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$\kappa$ -categorical

(Definition)

Let be a first order language and let be a set of -sentences. If $\kappa$ is a cardinal, then is said to be $\kappa$ -categorical if has a model of cardinality $\kappa$ and any two such models are isomorphic.

In other words, is categorical iff it has a unique model of cardinality $\kappa$ , to within isomorphism.

" $\kappa$ -categorical" is owned by Evandar.

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Keywords:

model theory, logic

Attachments:: countably categorical structures (Derivation) by amador

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Cross-references: isomorphism, iff, categorical, isomorphic, cardinality, cardinal, first order language

This is version 1 of $\kappa$ -categorical, born on 2002-08-29.
Object id is 3390, canonical name is KappaCategorical.
Accessed 1959 times total.

Classification:

AMS MSC:

03C35 (Mathematical logic and foundations :: Model theory :: Categoricity and completeness of theories)

Pending Errata and Addenda

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