TY - JOUR
T1 - S-forcing, I. A "black-box" theorem for morasses, with applications to super-Souslin trees
AU - Shelah, S.
AU - Stanley, L.
PY - 1982/9
Y1 - 1982/9
N2 - 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 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+SHא 2{long rightwards double arrow}א2 is (inaccessible)L.
AB - 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 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+SHא 2{long rightwards double arrow}א2 is (inaccessible)L.
UR - http://www.scopus.com/inward/record.url?scp=51249186732&partnerID=8YFLogxK
U2 - 10.1007/BF02761942
DO - 10.1007/BF02761942
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AN - SCOPUS:51249186732
SN - 0021-2172
VL - 43
SP - 185
EP - 224
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 3
ER -