We show that under the axiom there is no uniformly completely Ramsey null set of size . In particular, this holds in the iterated perfect set model. This answers a question of U. Darji.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-2-4,
author = {Andrzej Nowik},
title = {Possibly there is no uniformly completely Ramsey null set of size $2^{$\omega$}$
},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {251-258},
zbl = {1014.03049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-2-4}
}
Andrzej Nowik. Possibly there is no uniformly completely Ramsey null set of size $2^{ω}$
. Colloquium Mathematicae, Tome 91 (2002) pp. 251-258. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm93-2-4/