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For any xed integer R ≥ 2 we characterise the typical structure of undi-rected graphs with vertices 1,. .. , n and maximum degree R, as n tends to innity. 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.

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)

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 automor-phisms, the automorphism group is (Z2) i for some i ≤ (m + 1)/2; and if some relation symbol has arity at least 3, then the… (More)

- Ove Ahlman, Vera Koponen
- 2015

We study denable sets D of SU-rank 1 in M eq , where M is a countable homogeneous and simple structure in a language with nite relational vocabulary. Each such D can be seen as a `canonically embedded structure', which inherits all relations on D which are denable in M eq , and has no other denable relations. Our results imply that if no relation symbol of… (More)

- Vera Koponen, Ove Ahlman
- 2012

A zero-one law for l-colourable structures with a vectorspace pregeometry Ove Ahlman A zero-one law for l-colourable structures with a vectorspace pregeometry Ove Ahlman

A probability distribution can be given to the set of isomorphism classes of models with universe {1,. .. , n} of a sentence in rst-order logic. We study the entropy of this distribution and derive a result from the 0-1 law for rst-order sentences.

We study a class C of ℵ 0-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)

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