Related papers: Special filters in bounded lattices
Our results in this paper increase the model-theoretic precision of a widely used method for building ultrafilters, and so advance the general problem of constructing ultrafilters whose ultrapowers have a precise degree of saturation. We…
Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…
Since for the classification of finite (congruence-)simple semirings it remains to classify the additively idempotent semirings, we progress on the characterization of finite simple additively idempotent semirings as semirings of…
We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…
Powdered materials of sizes ranging from nanometers to microns are widely used in materials science and are carefully selected to enhance the performance of a matrix. Fillers have been used in order to improve, among the others, mechanical,…
A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…
We completely determine all distributive, codistributive, standard, costandard, and neutral elements in the lattice of overcommutative semigroup varieties, thus correcting a gap contained in an earlier article by the second author.
We use information theory to study recovering sets $\R_L$ and strongly cancellative sets $\C_L$ on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in [1], [3] and [5]. We…
It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
This paper is the first part of a study devoted to description of modular elements in the lattices of semigroup and epigroup varieties. We provide strengthened necessary and sufficient conditions under which a semigroup or epigroup variety…
In continuous first-order logic, the union of definable sets is definable but generally the intersection is not. This means that in any continuous theory, the collection of $\varnothing$-definable sets in one variable forms a…
We prove the following result: Let K be a lattice, let D be a distributive lattice with zero, and let $\phi$: Con K $\to$ D be a {∨, 0}-homomorphism, where Conc K denotes the {∨, 0}-semilattice of all finitely generated…
We initiate the study of general metric lattices in the context of the model theory of metric structures. As an application we develop a theory of pseudo-finite limits of partition lattices and connect this theory with the theory of…
For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, --The class of all finite…
The preparation of many composites requires the intermixing of several macromolecular fluids along with the addition of solid filler particles. These fillers are usuallly polydisperse and there is an extensive experimental evidence that…
We develop the theory of mixed finite elements in terms of special inverse systems of complexes of differential forms, defined over cellular complexes. Inclusion of cells corresponds to pullback of forms. The theory covers for instance…
The possibility is considered for the formation in optical lattices of a heterogeneous state characterized by a spontaneous mesoscopic separation of the system into the spatial regions with different atomic densities. It is shown that such…
Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…
The present paper deals with complemented lattices where, however, a unary operation of complementation is not explicitly assumed. This means that an element can have several complements. The mapping $^+$ assigning to each element $a$ the…