… Two natural cardinals come with the notion of a pseudointersection. One is the pseudointersection
… So we have shown that f ’ X is a pseudointersection of the ground model club filter. □ …

… For this purpose we generalize some standard facts that hold in the countable case as well
as … We also establish some of the natural inequalities between the generalized characteristics …

… pseudointersections that preceded the proof of p = t. For instance we will show how
pseudointersections … The last chapter deals with the generalization of pseudointersections to …

… 7, we investigate pseudointersection and tower numbers … forcing has naturally defined
pseudointersection and tower numbers, … 7.2, we show that pseudointersection and tower numbers …

… elements are denoted as pseudo-intersections. Pseudo-intersections are intersections of …
By decomposing the description into subunits, pseudo-intersections among the data sets …

… family of clubs in κ with no pseudointersection of size κ. Build a … pseudointersection of Eβ
= {Dα : α<β}∪{Cα : α ≤ β} (note the closure of a pseudointersection is still a pseudointersection)…

… The pseudointersection number p and the tower number t … B, that is there is no
pseudointersection S of A almost including … Bj : j E wl}) be a family of pseudointersections of A = {Ai …

… Arriving at η we choose a pseudointersection A of cardinality λ for the family {ran(fξ) : ξ<η}.
The existence of A is ensured by the fact that η < tλ. Now, for every α<λ we define: …

… , we also say that A ⊆ ω is a pseudointersection of F, A ⊆∗ F for all F ∈ F. A tower T is a
well-ordered family of subsets of ω with the FIP that has no infinite pseudointersection. …

… We define the pseudointersection of X with growth controlled by f to be the set … (notice that
Ps(X,f) is indeed a pseudointersection for the Xn, and a subset of X0), and we also define the “…