Cardinal Invariants Related to Density
Year: 2025
Type: article
Abstract: We investigate some variants of the splitting, reaping, and independence numbers defined using asymptotic density. Specifically, we give a proof of Con( $\mathfrak {i}<\mathfrak {s}_{1/2}$ ), Con( $\mathfrak {r}_{1/2}<\mathfrak {b}$ ), and Con( $\mathfrak {i}_*<2^{\aleph _0}$ ). This answers two questions raised in [5]. Besides, we prove the consistency of $\mathfrak {s}_{1/2}^{\infty } < $ non $(\mathcal {E})$ and cov $(\mathcal {E}) < \mathfrak {r}_{1/2}^{\infty }$ , where $\mathcal {E}$ is the $\sigma $ -ideal generated by closed sets of measure zero.
Source: Journal of Symbolic Logic
Author: DAVID VALDERRAMA
Institution: Universidad de Los Andes
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4413903076