P-Points and Preservation Theorems

Abstract

An important part of many independence proofs using iterated forcing, is to show that some property X is preserved (if satisfied by each iterand). We have dealt with such a problem (the ω ^ω-bounding property) and similar proofs can be worked out for several other examples. We give here a general context which serves for many examples (but unfortunately not for “adding no reals”). In fact there is more in common between the examples discussed later even than expressed by the stricter context suggested here (fine cover­ing model) (i.e., the use of trees T, T ∩ ⁿ ω finite )but the saving will be minimal.