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103:, proved several independently. Despite this, the literature still widely refers to the Ryll-Nardzewski theorem as a name for these conditions. The conditions included with the theorem vary between authors.
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The theory of any countably infinite structure which is homogeneous over a finite relational language is omega-categorical. More generally, the theory of the
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of any uniformly locally finite Fraïssé class is omega-categorical. Hence, the following theories are omega-categorical:
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Many conditions on a theory are equivalent to the property of omega-categoricity. In 1959
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Mathematical logic theory with exactly one countably infinite model up to isomorphism
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A Course in Model Theory: An
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Macpherson, Dugald (2011), "A survey of homogeneous structures",
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The theory of dense linear orders without endpoints (
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with infinite models, the following are equivalent:
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308:The theory of infinite linear spaces over any
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347:Hodges, Model Theory, p. 341.
586:. You can help Knowledge by
547:Introduction to Model Theory
297:Cantor's isomorphism theorem
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545:Rothmaler, Philipp (2000),
336:A primer of simple theories
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263:has a countable atomic and
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210:For every natural number
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25:omega-categorical theory
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582:-related article is a
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477:A shorter model theory
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