HIGHER INDEPENDENCE

Abstract We study higher analogues of the classical independence number on $\omega $ . For $\kappa regular uncountable, we denote by $i(\kappa )$ minimal size a maximal -independent family. establish ZFC relations between and standard some cardinal characteristics, e.g., $\mathfrak {r}(\kappa )\leq \mathfrak {i}(\kappa {d}(\kappa measurable, assuming that $2^{\kappa }=\kappa ^{+}$ construct family which remains after -support product $\lambda many copies -Sacks forcing. Thus, show consistency ^{+}=\mathfrak )=\mathfrak )<2^{\kappa }$ conclude paper with interesting open questions discuss difficulties regarding other natural approaches to independence.