Cardinal characteristics associated with small subsets of reals
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 Fσ measure zero sets. We show they are σ-ideals characterizing all small sets and Fσ 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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Rings
Modules
and Algebras
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- Fundamenta Mathematicae
- Publisher
- Institute of Mathematics, Polish Academy of Sciences
- Publication date
- 11 August 2026
- Language
- EN