Remarks on a paper of S. K. Bhattacharyya and B. K. Lahiri
Remarks on invariant descriptive set theory
Remarks on -fields without continuous measure
Remarks on σ-fields without continuous measures
Rothberger gaps in fragmented ideals
The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum...
Rudin-like sets and hereditary families of compact sets
We show that a comeager Π₁¹ hereditary family of compact sets must have a dense subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ℳ ₀-sets, the meagerness of ₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true sets.
Selected results on measurable selections
Selivanovski hard sets are hard
Let . For n ≥ 2, we prove that if Selivanovski measurable functions from to Z give as preimages of H all Σₙ¹ subsets of , then so do continuous injections.
Separating equivalence classes
Given a countable Borel equivalence relation, I introduce an invariant measuring how difficult it is to find Borel sets separating its equivalence classes. I evaluate these invariants in several standard generic extensions.
Sets with no uncountable Blackwell subsets
Sigma-idéaux polaires et ensembles d'unicité dans les groupes abéliens localement compacts
On étend au cadre des groupes abéliens localement compacts certains résultats obtenus notamment par G. Debs, R. Kaufman, A. Kechris, A. Louveau et J. Saint Raymond sur la structure des fermés d’unicité et d’unicité au sens large du cercle unité. On montre également que de très nombreuses familles de compacts issues de l’Analyse Harmonique sont exactement de troisième classe dans la hiérarchie de Baire. Comme application, on donne une démonstration simple de l’existence d’ensembles de Dirichlet qui...
Solution of a problem of Ulam on countable sequences of sets
Some additive properties of sets of real numbers
Some additive properties of special sets of reals
Some comments on infinite Boolean functions
We introduce infinite Boolean functions and investigate some of their properties.
Some connections between measure, indiscernibility and representation of cuts
Some examples in the theory of Borel sets
Some examples of true sets
Let K(X) be the hyperspace of a compact metric space endowed with the Hausdorff metric. We give a general theorem showing that certain subsets of K(X) are true sets.
Some relations between k-analytic sets and generalized Borel sets
Some remarks about Mycielski ideals