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We consider a set K = n∈N Kn of nite structures such that all members of Kn have the same universe, the cardinality of which approaches ∞ as n → ∞. Each structure in K may have a nontrivial underlying pregeometry and on each Kn we consider a probability measure, either the uniform measure, or what we call the dimension conditional measure. The main(More)
A systematic study is made, for an arbitrary finite relational language with at least one symbol of arity at least 2, of classes of nonrigid finite structures. The well known results that almost all finite structures are rigid and that the class of finite structures has a zero-one law are, in the present context, the first layer in a hierarchy of classes of(More)
For integers l ≥ 1, d ≥ 0 we study (undirected) graphs with vertices 1,. .. , n such that the vertices can be partitioned into l parts such that every vertex has at most d neighbours in its own part. The set of all such graphs is denoted Pn(l, d). We prove a labelled rst-order limit law, i.e., for every rst-order sentence ϕ, the proportion of graphs in(More)
Suppose that M is countable, binary, primitive, homogeneous, simple and 1-based. We prove that the SU-rank of the complete theory of M is 1. It follows that M is a random structure. The conclusion that M is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that(More)