The authors give a ZFC example for a space with $\text{\it Split}\kern 0.8pt (\Omega , \Omega )$ but not $\text{\it Split}\kern 0.8pt (\Lambda , \Lambda )$.
@article{118936,
author = {Winfried Just and Andreas Tanner},
title = {Splitting $\omega$-covers},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {38},
year = {1997},
pages = {375-378},
zbl = {0887.04001},
mrnumber = {1455505},
language = {en},
url = {http://dml.mathdoc.fr/item/118936}
}
Just, Winfried; Tanner, Andreas. Splitting $\omega$-covers. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 375-378. http://gdmltest.u-ga.fr/item/118936/
The combinatorics of open covers, Topology and its Applications, to appear. | Zbl 0870.03021
Descriptive Set Theory, North Holland, 1980. | MR 0561709
Set Theory, A.K. Peters, 1995. | MR 1350295
A model without ultrafilters, Bull. Acad. Polon. Sci. 25 (1977), 4 329-331. (1977) | MR 0476510 | Zbl 0365.02054