We characterize the class of definable families of countable sets for which there is a single countable definable set intersecting every element of the family.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-1-2, author = {Andr\'es Eduardo Caicedo and John Daniel Clemens and Clinton Taylor Conley and Benjamin David Miller}, title = {Definability of small puncture sets}, journal = {Fundamenta Mathematicae}, volume = {215}, year = {2011}, pages = {39-51}, zbl = {1254.03085}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-1-2} }
Andrés Eduardo Caicedo; John Daniel Clemens; Clinton Taylor Conley; Benjamin David Miller. Definability of small puncture sets. Fundamenta Mathematicae, Tome 215 (2011) pp. 39-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm215-1-2/