Related papers: Lovely pairs for independence relations
We introduce the concept of a Gr\"obner nice pair of ideals in a polynomial ring and we present some applications.
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.
We give an abstract framework to transfer generalized amalgamation from a simple theory to another, and we apply it to theories of lovely pairs and of bounded PAC structures. We show in particular that bounded pseudo-algebraically closed…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
The randomization of a complete first order theory $T$ is the complete continuous theory $T^R$ with two sorts, a sort for random elements of models of $T$, and a sort for events in an underlying probability space. We study various notions…
We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a…
We presents an independence relation on sets, one can define dimension by it, assuming that we have an abstract elementary class with a forking notion that satisfies the axioms of a good frame minus stability.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…
We initiate a systematic study of \emph{generic stability independence} and introduce the class of \emph{treeless theories} in which this notion of independence is particularly well-behaved. We show that the class of treeless theories…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
The traditional Pi-theorem tells us that for any dimensionally invariant relation there exists a full set of independent dimensionless "Pi groups" which can be used to nondimensionalise the relation. In this paper, we seek to understand…
This paper is about producing a new kind of the pairs which we call it MS-pairs. To produce these pairs, we use an algorithm for dividing a natural number $x$ by two for two arbitrary numbers and consider their related graphs. We present…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
We introduce the concepts of a pair of valuations and a good generating set and show how they can be used to prove geometric properties of soluble groups.
Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a…
We study properties that allow first-order theories to be disjointly combined, including stable infiniteness, shininess, strong politeness, and gentleness. Specifically, we describe a Galois connection between sets of decidable theories,…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
Normal ideals on regular uncountable cardinals are familiar objects. We investigate ideals that are pleasant--while a normal ideal is closed under arbitrary diagonal unions, a pleasant ideal is closed only under diagonal unions indexed by…
We offer a more general Bailey pair than one that was proved in two different papers by two different methods [5, 12].