We give a different proof of the well-known fact that any uncountable family of analytic subsets of a Polish space with the point-finite intersection property must contain a subfamily whose union is not analytic. Our approach is based on the Kunen-Martin theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-11, author = {Pandelis Dodos}, title = {Stable families of analytic sets}, journal = {Colloquium Mathematicae}, volume = {96}, year = {2003}, pages = {277-281}, zbl = {1044.03033}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-11} }
Pandelis Dodos. Stable families of analytic sets. Colloquium Mathematicae, Tome 96 (2003) pp. 277-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm98-2-11/