We show that (1) stick plus $\mathrm{cov}\left(\mathscr{M}\right)>\aleph_1$ implies the existence of a destructible gap and (2) $\clubsuit$ plus $\mathrm{cof}\left(\mathscr{M}\right)=\aleph_1$ implies the existence of a destructible gap.
Publié le : 2005-10-14
Classification:
$\clubsuit$,
stick,
cardinal invariants of the meager ideal,
destructible gaps,
03E05,
03E35
@article{1150287311,
author = {YORIOKA, Teruyuki},
title = {Combinatorial principles on $\bm{\omega\_1}$, cardinal invariants of the meager ideal and destructible gaps},
journal = {J. Math. Soc. Japan},
volume = {57},
number = {4},
year = {2005},
pages = { 1217-1228},
language = {en},
url = {http://dml.mathdoc.fr/item/1150287311}
}
YORIOKA, Teruyuki. Combinatorial principles on $\bm{\omega_1}$, cardinal invariants of the meager ideal and destructible gaps. J. Math. Soc. Japan, Tome 57 (2005) no. 4, pp. 1217-1228. http://gdmltest.u-ga.fr/item/1150287311/