# The higher Cichon diagram in the degenerate case

## TL;DR

This paper investigates the relationships between various cardinal invariants related to the higher meager ideal at a regular uncountable cardinal, providing characterizations and models that clarify their possible values in the degenerate case.

## Contribution

It offers a complete characterization of add(M_kappa) and cof(M_kappa) in terms of other invariants and constructs models showing the range of non(M_kappa) values, addressing open questions in the field.

## Key findings

- Characterization of add(M_kappa) and cof(M_kappa) in terms of cov(M_kappa), non(M_kappa), and unbounding/dominating numbers.
- Models demonstrating no restrictions on non(M_kappa) in the degenerate case 2^{<kappa} > kappa.
- Open question remaining for cof(M_kappa) values.

## 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.