Un crible généralisé
Une démonstration du théorème de séparation des ensembles analytiques
Une démonstration du théorème de Souslin-Lusin
Une remarque sur le schéma de Bernoulli et quelques extensions
Une remarque sur les espaces sousliniens de Bourbaki
Uniformly completely Ramsey sets
Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also hold for uniformly...
Universally measurable sets in generic extensions
A subset of a topological space is said to be universally measurable if it is measured by the completion of each countably additive σ-finite Borel measure on the space, and universally null if it has measure zero for each such atomless measure. In 1908, Hausdorff proved that there exist universally null sets of real numbers of cardinality ℵ₁, and thus that there exist at least such sets. Laver showed in the 1970’s that consistently there are just continuum many universally null sets of reals....