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/