Pair-splitting, pair-reaping and cardinal invariants of Fσ-ideals

Abstract

We investigate the pair-splitting number 𝔰_pair which is a variation of splitting number, pair-reaping number 𝔯_pair which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of F_σ 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.