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/