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

S. Shelah*, L. Stanley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

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 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.

Original languageEnglish
Pages (from-to)185-224
Number of pages40
JournalIsrael Journal of Mathematics
Volume43
Issue number3
DOIs
StatePublished - Sep 1982

Fingerprint

Dive into the research topics of 'S-forcing, I. A "black-box" theorem for morasses, with applications to super-Souslin trees'. Together they form a unique fingerprint.

Cite this