
doi: 10.2178/jsl.7803010
AbstractUsing square sequences, a stationary subsetSTof אω1+1is constructed from a treeTof heightω1, uniformly inT. Under suitable hypotheses, adding a closed unbounded subset toSTrequires adding a cofinal branch toTor collapsing at least one ofω1, אω1, and אω1+1. An application is that in ZFC there is no parameter free definition of the family of subsets of אω1+1that have a closed unbounded subset in someω1, אω1, and אω1+1preserving outer model.
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