A graph is n-e.c. (n-existentially closed) if for every pair of subsets A, B of vertex set V of the graph such that A∩B = ∅ and |A|+ |B| = n, there is a vertex z not in A∪B joined to each vertex of A and no vertex of B. Few explicit families of n-e.c. are known for n > 2. In this short note, we give a new construction of 3-e.c. graphs using the notion of quadrance in the finite Euclidean space Zp.

We give an explicit AE-axiomatization of the almost sure theories of sparse random graphs G(n, n−α) of Shelah-Spencer. In the process we give a method of constructing extensions of graphs whose ‘relative dimension’ is negative, but arbitrarily small. We describe the existentially closed and locally finite models of the theory and produce types of dimension zero. We offer a useful characterizati...

We present a novel interpolation algorithm for effectively propositional logic (epr), a decidable fragment of first-order logic that enjoys a small-model property. epr is a powerful fragment of quantified formulas that has been used to model and verify a range of programs, including heap-manipulating programs and distributed protocols. Our interpolation technique samples finite models from two ...

The notions we study in this paper, those of existentially-atomic structure and effectively existentially-atomic structure, are not really new. The objective of this paper is to single them out, survey their properties from a computability-theoretic viewpoint, and prove a few new results about them. These structures are the simplest ones around, and for that reason alone, it is worth analyzing ...

Fourth International Conference Artificial Intelligence and Symbolic Computation, Plattsburgh, NY, September 1998. LNAI 1476, pp. 247–258, Springer Verlag, 1998. Abstract. We present an automatic approach for instantiating existentially quantified variables in inductive specifications proofs. Our approach uses first-order meta-variables in place of existentially quantified variables and combine...

Companions of the field rational numbers and a real-closed algebraic expansion are studied. The description existentially closed companions refers to study classical structures. general theory companions, built on basis Fraisse's classes in works A.T. Nurtazin, is included theories model theory. basic concept companion: two models same signature called if for any finite submodel one them, there...