Related papers: Lovely pairs for independence relations
The FKG theorem says that the POSITIVE LATTICE CONDITION, an easily checkable hypothesis which holds for many natural families of events, implies POSITIVE ASSOCIATION, a very useful property. Thus there is a natural and useful theory of…
We formalize the general principle of significance with respect to binary relations which is a universal tool for description and analysis of various situations in and apart from mathematics. We derive the basic properties and focus on a…
We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…
Inspired by Terao's freeness conjecture, we examine Ziegler pairs, which are pairs of hyperplane arrangements that share the same underlying matroid but have different modules of logarithmic derivations. In this paper, we present a general…
We introduce the concept of a Girard couple, which consists of two (not necessarily unital) quantales linked by a strong form of duality. The two basic examples of Girard couples arise in the study of endomorphism quantales and of the…
In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one…
We introduce the affine Vogan diagrams of complex simple Lie algebras. These are generalizations of Vogan diagrams, and we study the involutions represented by them. We apply these diagrams to study the symmetric pairs, in particular the…
The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…
Consider tuples of separable algebras over a common local or global number field, related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best…
We consider several ways of decomposing models into parts of bounded size forming a congruence over a base, and show that admitting any such decomposition is equivalent to mutual algebraicity at the level of theories. We also show that a…
We give an introduction to the theory of wonderful G-varieties, with many examples when G is simple of type F4. We present results and open problems about these varieties: on their classification, on their isotropy groups, on morphisms…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
A generalized model of games is proposed, in which cooperative games and non-cooperative games are special cases. Some games that are neither cooperative nor non-cooperative can be expressed and analyzed. The model is based on relationships…
We extend the classical associative PI-theory to Associative Pairs, and in doing so, we introduce related notions already present for algebras (and Jordan systems) as the ones of PI-element and PI-ideal, extended centroid and central…
In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them…
The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations…
The classical theorems relating integral binary quadratic forms and ideal classes of quadratic orders have been of tremendous importance in mathematics, and many authors have given extensions of these theorems to rings other than the…
Recently, we have endowed various categories of groups with topologies. The purpose of this paper is to introduce on these categories others topologies which are statistically more suitable to study well-known problems in groups theory. We…