Décompositions d'un intervalle réel et des ensembles de Cantor
Decompositions of the plane and the size of the continuum
We consider a triple ⟨E₀,E₁,E₂⟩ of equivalence relations on ℝ² and investigate the possibility of decomposing the plane into three sets ℝ² = S₀ ∪ S₁ ∪ S₂ in such a way that each intersects each -class in finitely many points. Many results in the literature, starting with a famous theorem of Sierpiński, show that for certain triples the existence of such a decomposition is equivalent to the continuum hypothesis. We give a characterization in ZFC of the triples for which the decomposition exists....
Dénombrements relatifs à une définition combinatoire de la continuité sur un graphe
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
Densité et dimension
Une partie de est appelée une classe de Vapnik-Cervonenkis si la croissance de la fonction est polynomiale; ces classes se trouvent être utiles en Statistique et en Calcul des Probabilités (voir par exemple Vapnik, Cervonenkis [V.N. Vapnik, A.YA. Cervonenkis, Theor. Prob. Appl., 16 (1971), 264-280], Dudley [R.M. Dudley, Ann. of Prob., 6 (1978), 899-929]).Le présent travail est un essai de synthèse sur les classes de Vapnik-Cervonenkis. Mais il contient aussi beaucoup de résultats nouveaux,...
Diamond and λ-systems
Disjoint refinement and related topics
Distance minimale entre partitions et préordonnances dans un ensemble fini
Distinguishing two partition properties of ω1
It is consistent that but .
Dualization of van Douwen diagram