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/