Set theory seminar -Forcing axioms and inner models IV

We proved Baumgartner’s result that under {sf BPFA}, every tree of height and size omega_1 is sealed in the sense that no outer model can add a new uncountable branch. From this we concluded Todorcevic’s result that under {sf BPFA} any forcing adding a subset of omega_1 either adds a real or else it collapses omega_2. We also drew some conclusions about inner models of {sf GCH}.

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