I isolate a simple condition that is equivalent to preservation of P-points in definable proper forcing.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-4,
author = {Jind\v rich Zapletal},
title = {Preserving P-points in definable forcing},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {145-154},
zbl = {1174.03022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-4}
}
Jindřich Zapletal. Preserving P-points in definable forcing. Fundamenta Mathematicae, Tome 205 (2009) pp. 145-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm204-2-4/