S-forcing, I. A “black-box” theorem for morasses, with applications to super-Souslin trees
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We formulate, for regular μ>ω, a “forcing principle” Sμ which we show is equivalent to the existence of morasses, thus providing a new and systematic method for obtaining applications of morasses. Various examples are given, notably that for infinitek, if 2 k =k + and there exists a (k +, 1)-morass, then there exists ak ++-super-Souslin tree: a normalk ++ tree characterized by a highly absolute “positive” property, and which has ak ++-Souslin subtree. As a consequence we show that CH+SHℵ 2⟹ℵ2 is (inaccessible)L.
KeywordsInitial Segment Restriction Property Amalgamation Property Elementary Embedding Infinite Cardinal
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