# Baire category of tall ideals

Problem. Is it consistent with ZFC that $$\mathfrak t=\omega_1$$ and each $$\omega_1$$-generated tall $$P$$-ideal is of the second Baire category?

(Asked 01.10.2016 by David Chodounsky at page 20 of Volume 1 of the Lviv Scottish Book).

Prize: A bottle of Becherovka.

• But Becherovka is not very tasty. :( – Asaf Karagila Mar 3 '17 at 14:26
• In small quantities it is a medicin :) – Lviv Scottish Book Mar 3 '17 at 17:30
• Some might argue that I'm not that kind of sick, though! ;) – Asaf Karagila Mar 5 '17 at 18:28
• I have added (infinite-combinatorics) - feel free to revert the edit if you think the tag does not fit, but to me small uncountable cardinals seem rather close to my understanding of infinitary combinatorics. (I was also considering adding (decriptive-set-theory) but it is probably not ideal fit here. – Martin Sleziak Sep 30 '17 at 9:24