Proper forcing remastered
Abstract
In these notes we present the method introduced by Neeman of generalized side conditions with two types of models. We then discuss some applications: the Friedman-Mitchell poset for adding a club in ω2 with finite conditions, Koszmider's forcing construction of a strong chain of length ω2 of functions from ω1 to ω1, and the Baumgartner-Shelah forcing construction of a thin very tall superatomic Boolean algebra.
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