Forcing with adequate sets of models as side conditions

摘要

We present a general framework for forcing on ω_2 with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on ω_2, adding a nonreflecting stationary subset of ω_2 ∩ cof(ω), and adding an ω_1-Kurepa tree.