On a construction of universally small sets. (English) Zbl 1044.03035

Zakrzewski, Piotr

Real Anal. Exch. 28(2002-2003), No. 1, 221-226 (2003).

Summary: We present a construction of an uncountable subset of the reals which belongs to every \(\sigma\)-ideal \(I\) on \(\mathbb{R}\) with the property that there is no uncountable family of disjoint Borel sets outside \(I\).

MSC:

03E15	Descriptive set theory
03E05	Other combinatorial set theory
28A05	Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
54E52	Baire category, Baire spaces

Keywords:

universally null set; universally meager set; universally small set; Fubini property; Ulam matrix