-multifunctions and their properties.
La détermination projective
La fonction logique de Hilbert à travers les «Grundlagen der Mathematik»
Laminations, or How to Build a Quantum-Logic-Valued Model of Set Theory.
Large cardinals and covering numbers
The paper is concerned with the computation of covering numbers in the presence of large cardinals. In particular, we revisit Solovay's result that the Singular Cardinal Hypothesis holds above a strongly compact cardinal.
Large cardinals and Dowker products
We prove that if there is a model of set-theory which contains no first countable, locally compact, scattered, countably paracompact space , whose Tychonoff square is a Dowker space, then there is an inner model which contains a measurable cardinal.
Large continuum, oracles
Our main theorem is about iterated forcing for making the continuum larger than ℵ2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing ℵ1,ℵ2 by λ, λ + (starting with λ = λ <λ > ℵ1). Well, we demand absolute c.c.c. So we get, e.g. the continuum is λ + but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a “partial” countable support iteration but it is c.c.c.
Large free set
Large semilattices of breadth three
A 1984 problem of S. Z. Ditor asks whether there exists a lattice of cardinality ℵ₂, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice follows from either one of two axioms that are known to be independent of ZFC, namely (1) Martin’s Axiom restricted to collections of ℵ₁ dense subsets in posets of precaliber ℵ₁, (2) the existence of a gap-1 morass. In particular, the existence of such a lattice is consistent...
Large small sets
Large variable systems of higher degrees in fuzzification process. Fuzzification of systems for technical and medical practice. II
Lattice valued algebras.
In this paper we propose a general approach to the theory of fuzzy algebras, while the early existing papers deal with a particular type of fuzzy structures as fuzzy groups, fuzzy ideals, fuzzy vector spaces and so on.
Lattice valued intuitionistic fuzzy sets
In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets.
Lattices of fuzzy objects.
L’autre axiome du choix
L’« axiome du choix simple » est le principe selon lequel on peut choisir un élément dans tout ensemble non vide. Cet « autre axiome du choix » a une histoire paradoxale et riche, dont la première partie de cet article recherche les traces et repère les enjeux. Apparaissent comme décisifs le statut de la théorie des ensembles dans les mathématiques intuitionnistes, mais aussi la tension croissante entre technicisation de la logique et réflexion épistémologique des mathématiciens. La deuxième partie...
L'Axiome de la paire dans le système de Zermelo.
Le problème de la mesure
Le problème des cardinaux singuliers
Lectures on ideal dichotomy
Left and right semi-uninorms on a complete lattice
Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary...