Combinatorial principles on $\bm{\omega_1}$, cardinal invariants of the meager ideal and destructible gaps

Abstract

We show that (1) stick plus $\mathrm{c}\mathrm{o}\mathrm{v}\left(ℳ\right)>{\mathrm{\aleph }}_1$ implies the existence of a destructible gap and (2) $\clubsuit$ plus $\mathrm{c}\mathrm{o}\mathrm{f}\left(ℳ\right)={\mathrm{\aleph }}_1$ implies the existence of a destructible gap.