Continued fractions, Fibonacci numbers, and some classes of irrational numbers.
Continuity Based on Convergence and Lower Complete Distributive Lattices instead of Directed Sets
Cyclically ordered sets
Definitions of finiteness based on order properties
A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Choice (AC) is assumed, is equivalent to stating that the set is finite; several such definitions have been studied over the years. In this article we introduce a framework for generating definitions of finiteness in a systematical way: basic definitions are obtained from properties of certain classes of binary relations, and further definitions are obtained from the basic ones by closing them under subsets...
Dénombrements systématiques de relations binaires externes
Dense orderings, partitions and weak forms of choice
We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context
Deux relations dénombrables, logiquement équivalentes pour le second ordre, sont isomorphes
Direct decomposability of tolerances and congruences on semigroups
Einführung der Normalfunktionen ... ohne Auswahlaxiom und ohne Regularitätsbedingung.
Einige Charakterisationen von Ketten
Éléments pour l'étude de relations localement définies («infra-relations»). Infra-ordres et relation ternaire d'intermédiarité
Dans les sciences de la nature, et en particulier dans les sciences du comportement, on rencontre fréquemment des relations caractérisées par des propriétés locales. Une famille très vaste de telles relations rassemble celles qui sont définies uniquement par des propriétés portant sur les ensembles d'éléments liés à un même élément, soit par la relation («points vus d'un même point»), soit par son inverse («points d'où l'on voit un même point»). A tout type de relation correspondent ainsi plusieurs...
Entscheidungsprobleme der Theorie zweier Äquivalenzrelationen mit beschränkter Zahl vоn Elementen in den Klassen
Existence theorems for commutative diagrams.
Families of sets and functions
Finite Equations in n Unknowns
Fixed Points Of Monotone Multifunctions In Partially Ordered Sets
Fuzziness and fuzzy equality
Fuzzy relation equation under a class of triangular norms: A survey and new results.
By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations. Considering a remarkable class of triangular norms, for such type of equations defined on finite sets, we characterize the upper an lower solutions.We also characterize the solutions posessing a minimal fuzziness measure of Yager valued with respect to a triangular...
Generalized projections of Borel and analytic sets
For a σ-ideal I of sets in a Polish space X and for A ⊆ , we consider the generalized projection (A) of A given by (A) = x ∈ X: Ax ∉ I, where =y ∈ X: 〈x,y〉∈ A. We study the behaviour of with respect to Borel and analytic sets in the case when I is a -supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [ for a wide class of -supported σ-ideals.
Homogeneous permutations.