We investigate the pair-splitting number 𝔰pair which is a variation of splitting number, pair-reaping number 𝔯pair which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of Fσ ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not locally Katětov-minimal among ideals not satisfying Fatou's lemma.
"Pair-splitting, pair-reaping and cardinal invariants of Fσ-ideals." J. Symbolic Logic 75 (2) 661 - 677, June 2010. https://doi.org/10.2178/jsl/1268917498