S-forcing, I. A "black-box" theorem for morasses, with applications to super-Souslin trees

We formulate, for regular μ>ω, a "forcing principle" S_μ 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 infinite k, if 2 ^k =k ⁺ and there exists a (k ⁺, 1)-morass, then there exists a k ⁺⁺-super-Souslin tree: a normal k ⁺⁺ tree characterized by a highly absolute "positive" property, and which has a k ⁺⁺-Souslin subtree. As a consequence we show that CH+SH_{א 2}{long rightwards double arrow}א₂ is (inaccessible)^L.