Weak-join of matriods
When is the orbit algebra of a group an integral domain ? Proof of a conjecture of P.J. Cameron
Cameron introduced the orbit algebra of a permutation group and conjectured that this algebra is an integral domain if and only if the group has no finite orbit. We prove that this conjecture holds and in fact that the age algebra of a relational structure R is an integral domain if and only if R is age-inexhaustible. We deduce these results from a combinatorial lemma asserting that if a product of two non-zero elements of a set algebra is zero then there is a finite common tranversal of their...
Z specification of object oriented constraint programs.
Object oriented constraint programs (OOCPs) emerge as a leading evolution of constraint programming and artificial intelligence, first applied to a range of industrial applications called configuration problems. The rich variety of technical approaches to solving configuration problems (CLP(FD), CC(FD), DCSP, Terminological systems, constraint programs with set variables, . . . ) is a source of difficulty. No universally accepted formal language exists for communicating about OOCPs, which makes...
Zero-one laws for graphs with edge probabilities decaying with distance. Part II
Let Gₙ be the random graph on [n] = 1,...,n with the probability of i,j being an edge decaying as a power of the distance, specifically the probability being , where the constant α ∈ (0,1) is irrational. We analyze this theory using an appropriate weight function on a pair (A,B) of graphs and using an equivalence relation on B∖A. We then investigate the model theory of this theory, including a “finite compactness”. Lastly, as a consequence, we prove that the zero-one law (for first order logic)...
Zero-one laws for graphs with edge probabilities decaying with distance. Part I
Let Gₙ be the random graph on [n] = 1,...,n with the possible edge i,j having probability for j ≠ i, i+1, i-1 with α ∈ (0,1) irrational. We prove that the zero-one law (for first order logic) holds..
Нормальность хорновых теорий с немаксимальным спектром
О полурешетках вычислимых индексаций классов конструктивных моделей
Об ошибке в статье И.И. Жегалкина "Проблема разрешимости на конечных классах"