We present a theorem which generalizes some known theorems on the existence of nonmeasurable (in various senses) sets of the form X+Y . Some additional related questions concerning measure, category… (More)

We study some set-theoretic properties of Schmidt’s σ-ideal on R, emphasizing its analogies and dissimilarities with both the classical σ-ideals on R of Lebesgue measure zero sets and of Baire first… (More)

We study relationships between classes of special subsets of the reals (e.g. meager-additive sets, γ-sets, C′′-sets, λ-sets) and the ideals related to the forcing notions of Laver, Mathias, Miller… (More)

The existence of such a function is independent from ZFC. Recall that for an ideal I, we define non(I) = min{|X| : X 6∈ I}. The following fact shows that it is consistent that an Erdös – Sierpiński… (More)

We construct a σ-ideal of subsets of the Cantor space which is productive but does not have the Weak Fubini Property. In the construction we use a combinatorial lemma which is of its own interest.

We construct Bernstein sets in R having some additional algebraic properties. In particular, solving a problem of Kraszewski, RaÃlowski, Szczepaniak and Żeberski, we construct a Bernstein set which… (More)

Edmund Ben Ami 2 Marek Balcerzak 2 Iryna Banakh 2 Taras Banakh 4 Christina Brech 6 Rafa l Filipów 7 David Gauld 7 Szymon G la̧b 7 Olena Hryniv 7 Jakub Jasinski 8 Jan Kraszewski 8 Wies law Kubís 8… (More)

We discuss the question of which properties of smallness in the sense of measure and category (e.g. being a universally null, perfectly meager or strongly null set) imply the properties of smallness… (More)