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oligomorphic permutation group
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(Definition)
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A permutation group acting on a countably infinite set is called oligomorphic, if it has finitely many orbits of  -tuples, for all  .
Ryll-Nardzewski, Engeler, and Svenonius proved that a countably infinite first-order structure has an oligomorphic automorphism group if and only if the structure is  -categorical.
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"oligomorphic permutation group" is owned by amador.
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(view preamble)
Cross-references: structure, orbits, countably infinite, permutation group
There is 1 reference to this entry.
This is version 3 of oligomorphic permutation group, born on 2005-05-12, modified 2005-05-12.
Object id is 7044, canonical name is OligomorphicPermutationGroup.
Accessed 1380 times total.
Classification:
| AMS MSC: | 03C35 (Mathematical logic and foundations :: Model theory :: Categoricity and completeness of theories) |
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Pending Errata and Addenda
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