Cardinal characteristics associated with small subsets of reals
Fundamenta Mathematicae
MSC: Primary 03E17; Secondary 03E35, 03E05, 03E15
DOI: 10.4064/fm250317-14-3
Published online: 11 August 2026
Abstract
Inspired by Bartoszyński’s work on small sets, we introduce a new ideal defined by interval partitions on natural numbers and summable sequences of positive reals. Similarly, we present another ideal that relies on Bartoszyński’s and Shelah’s representation of $F_\sigma $ measure zero sets. We show they are $\sigma $-ideals characterizing all small sets and $F_\sigma $ measure zero sets. We also study the cardinal characteristics associated with the ideals introduced. We use them to describe invariants of measure, discuss their connection to Cichoń’s diagram, and present related consistency results.
