Israel Journal of Mathematics

, Volume 43, Issue 3, pp 185–224 | Cite as

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

  • S. Shelah
  • L. Stanley


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+SH 2⟹ℵ2 is (inaccessible)L.


Initial Segment Restriction Property Amalgamation Property Elementary Embedding Infinite Cardinal 
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Copyright information

© Hebrew University 1982

Authors and Affiliations

  • S. Shelah
    • 1
    • 2
  • L. Stanley
    • 1
    • 2
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Maths Pures-Les CezeauxUniversité de Clermont IIAubiereFrance

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