Characterizations of commuting relations
Characterizing the powerset by a complete (Scott) sentence
This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing previous work of the author. A cardinal κ is characterized by a Scott sentence if has a model of size κ, but no model of size κ⁺. The main question in this paper is the following: Are the characterizable cardinals closed under the powerset operation? We prove that if is characterized by a Scott sentence, then is (homogeneously) characterized by a Scott sentence, for all 0 < β₁ < ω₁....
Characterizing tolerance trivial finite algebras
An algebra is tolerance trivial if where is the lattice of all tolerances on . If contains a Mal’cev function compatible with each , then is tolerance trivial. We investigate finite algebras satisfying also the converse statement.
Charakter von Mengensystemen.
Choice Mappings of Certain Classes of Finite Sets.
Choice principles in elementary topology and analysis
Many fundamental mathematical results fail in ZF, i.e., in Zermelo-Fraenkel set theory without the Axiom of Choice. This article surveys results — old and new — that specify how much “choice” is needed precisely to validate each of certain basic analytical and topological results.
Choice principles in Węglorz’ models
Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.
Choosing an attacker by a local derivation
Chromatic number of the product of graphs, graph homomorphisms, antichains and cofinal subsets of posets without AC
In set theory without the axiom of choice (AC), we observe new relations of the following statements with weak choice principles. If in a partially ordered set, all chains are finite and all antichains are countable, then the set is countable. If in a partially ordered set, all chains are finite and all antichains have size , then the set has size for any regular . Every partially ordered set without a maximal element has two disjoint cofinal sub sets – CS. Every partially ordered set...
Circulant Boolean relation matrices
Class preserving mappings of equivalence systems
By an equivalence system is meant a couple where is a non-void set and is an equivalence on . A mapping of an equivalence system into is called a class preserving mapping if for each . We will characterize class preserving mappings by means of permutability of with the equivalence induced by .
Classes de Wadge potentielles et théorèmes d'uniformisation partielle
On cherche à donner une construction aussi simple que possible d'un borélien donné d'un produit de deux espaces polonais. D'où l'introduction de la notion de classe de Wadge potentielle. On étudie notamment ce que signifie "ne pas être potentiellement fermé", en montrant des résultats de type Hurewicz. Ceci nous amène naturellement à des théorèmes d'uniformisation partielle, sur des parties "grosses", au sens du cardinal ou de la catégorie.
Classes of Dedekind finite cardinals
Classes of fuzzy measures and distortion
Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.
Classical hierarchies form a modern standpoint. Part III. BP-sets
Classical hierarchies from a modern standpoint. Part I. C-sets
Classical hierarchies from a modern standpoint. Part II. R-sets
Classification and extension by the transfinite induction
Classification of the regular De Morgan algebras of fuzzy sets.
A characterization of regular lattices of fuzzy sets and their isomorphisms is given in Part I. A characterization of involutions on regular lattices of fuzzy sets and the isomorphisms of De Morgan algebras of fuzzy sets is given in Part II. Finally all classes of De Morgan algebras of fuzzy sets with respect to isomorphisms are completely described.
Classifying Projective-like Hierarchies