The higher Cichon diagram in the degenerate case

Abstract

For a regular uncountable cardinal kappa, we discuss the order relationship between the unbounding and dominating numbers on kappa and cardinal invariants of the higher meager ideal M_kappa. In particular, we obtain a complete characterization of add(M_kappa) and cof(M_kappa) in terms of cov(M_kappa) and non(M_kappa) and unbounding and dominating numbers, and we provide models showing that there are no restrictions on the value of non(M_kappa) in the degenerate case 2^{<kappa} > kappa except 2^{<kappa} leq non(M_kappa) leq 2^kappa. The corresponding question for cof(M_kappa) remains open. Our results answer questions of joint work of the author with Brooke-Taylor, Friedman, and Montoya.