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Journals and Conferences
We consider a setK = ⋃ 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)
We study nite l-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are rst randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are… (More)
We study a class C of א0-categorical simple structures such that every M in C has uncomplicated forking behavior and such that definable relations in M which do not cause forking are independent in a sense that is made precise; we call structures in C independent. The SU-rank of such M may be n for any natural number n > 0. The most well-known unstable… (More)
For any xed integer R ≥ 2 we characterise the typical structure of undirected graphs with vertices 1, . . . , n and maximum degree R, as n tends to in nity. The information is used to prove that such graphs satisfy a labelled limit law for rst-order logic. If R ≥ 5 then also an unlabelled limit law holds.
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)
We work with a nite relational vocabulary with at least one relation symbol with arity at least 2. Fix any integer m > 1. For almost all nite structures (labelled or unlabelled) such that at least m elements are moved by some automorphisms, the automorphism group is (Z2) for some i ≤ (m+1)/2; and if some relation symbol has arity at least 3, then the… (More)
Suppose thatM is an in nite structure with nite relational vocabulary such that every relation symbol has arity at most 2. IfM is simple and homogeneous then its complete theory is supersimple with nite SU-rank which cannot exceed the number of complete 2-types over the empty set.
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)
Let V be a nite relational vocabulary in which no symbol has arity greater than 2. Let M be countable V -structure which is homogeneous, simple and 1based. The rst main result says that if M is, in addition, primitive, then it is strongly interpretable in a random structure. The second main result, which generalizes the rst, implies (without the assumption… (More)