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- W2023561941 abstract "We prove, by a probabilistic argument, that a class of ω-categorical structures, on which algebraic closure defines a pregeometry, has the finite submodel property. This class includes any expansion of a pure set or of a vector space, projective space or affine space over a finite field such that the new relations are sufficiently independent of each other and over the original structure. In particular, the random graph belongs to this class, since it is a sufficiently independent expansion of an infinite set, with no structure. The class also contains structures for which the pregeometry given by algebraic closure is non-trivial." @default.
- W2023561941 created "2016-06-24" @default.
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- W2023561941 date "2006-05-01" @default.
- W2023561941 modified "2023-10-18" @default.
- W2023561941 title "The finite submodel property and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif display=inline overflow=scroll><mml:mi>ω</mml:mi></mml:math>-categorical expansions of pregeometries" @default.
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- W2023561941 doi "https://doi.org/10.1016/j.apal.2005.05.013" @default.
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