The finite submodel property and ω-categorical expansions of pregeometries
2006 (English)In: Annals of Pure and Applied Logic, ISSN 0168-0072, E-ISSN 1873-2461, Vol. 139, no 1-3, 201-229 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2006. Vol. 139, no 1-3, 201-229 p.
Model theory, Finite submodel property, Pregeometry, Random structure
Algebra and Logic
IdentifiersURN: urn:nbn:se:uu:diva-83172DOI: 10.1016/j.apal.2005.05.013OAI: oai:DiVA.org:uu-83172DiVA: diva2:111079