The iteration theorems we presented so far give a wealth of results about the subsets of ω and, to some extent, ω1. For example, a typical result obtained by the application of iterated proper forcing is the construction of a model in which ω1 = □ < ■ = ω2, where □ and ■ are cardinal invariants of the continuum. One can consult the book [3] by Tomek Bartoszyński and Haim Judah for various instances of this method. The difficulties of generalising this context to the larger cardinals, even of the form κ+ for κ satisfying κ<κ = κ, turn out to be substantial. In the above mentioned exposition of iterated forcing Baumgartner [5, §4] wrote