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[parent] countably categorical structures (Derivation)

A countably infinite structure is called countably categorical (also called $ \omega$-categorical, or $ \aleph_0$-categorical) if all countable models of its first-order theory are isomorphic.

Ryll-Nardzewski, Engeler, and Svenonius proved that a countable structure is $ \omega$-categorical if and only if it has an oligomorphic automorphism group.



"countably categorical structures" is owned by amador.
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See Also: oligomorphic permutation group, oligomorphic permutation group

Other names:  $\aleph_0$-categorical, $\omega$-categorical

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Cross-references: oligomorphic automorphism group, isomorphic, first-order theory, countable, categorical, structure, countably infinite

This is version 2 of countably categorical structures, born on 2005-05-12, modified 2005-05-12.
Object id is 7045, canonical name is CountablyCategoricalStructures.
Accessed 1880 times total.

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