We answer several questions of V. Tkachuk [Fund. Math. 186 (2005)] by showing that
∙ there is a ZFC example of a first countable, 0-dimensional Hausdorff space with no point-countable π-base (in fact, the minimum order of a π-base of the space can be made arbitrarily large);
∙ if there is a κ-Suslin line then there is a first countable GO-space of cardinality κ⁺ in which the order of any π-base is at least κ;
∙ it is consistent to have a first countable, hereditarily Lindelöf regular space having uncountable π-weight and ω₁ as a caliber (of course, such a space cannot have a point-countable π-base).