ABSTRACT

D e f i n it io n 1.1. Given a class Γ of partially ordered sets (henceforth posets for short), the bounded forcing axiom for Γ, which I will denote by BFA{T), is the assertion that for every P e Γ and every collection (Af : i < coi) of maximal antichains of P all of which have size at most Ni there is a filter G C P intersecting each A im G is said to be generic for {Ai : i < ω i}.