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

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Abstract

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 2k=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.

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Author notes

  1. L. Stanley

    Present address: Department of Mathematics, Lehigh University, 18015, Bethlehem, PA, USA

Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    S. Shelah & L. Stanley

  2. Maths Pures-Les Cezeaux, Université de Clermont II, 63170, Aubiere, France

    S. Shelah & L. Stanley

Authors
  1. S. Shelah
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  2. L. Stanley
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Additional information

This author thanks the US-Israel Binational Science Foundation for partial support of this research.

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Shelah, S., Stanley, L. S-forcing, I. A “black-box” theorem for morasses, with applications to super-Souslin trees. Israel J. Math. 43, 185–224 (1982). https://doi.org/10.1007/BF02761942

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  • DOI: https://doi.org/10.1007/BF02761942

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