The higher Cichon diagram in the degenerate case
Logic
2022-02-03 v2
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.
Keywords
Cite
@article{arxiv.1907.03111,
title = {The higher Cichon diagram in the degenerate case},
author = {Joerg Brendle},
journal= {arXiv preprint arXiv:1907.03111},
year = {2022}
}
Comments
13 pages. Revised version. Major changes in section 1