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A Forcing Axiom Deciding the Generalized Souslin Hypothesis

  • Chris Lambie-Hanson (a1) and Assaf Rinot (a1)

Abstract

We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\unicode[STIX]{x1D706}$ , if $\unicode[STIX]{x1D706}^{++}$ is not a Mahlo cardinal in Gödel’s constructible universe, then $2^{\unicode[STIX]{x1D706}}=\unicode[STIX]{x1D706}^{+}$ entails the existence of a $\unicode[STIX]{x1D706}^{+}$ -complete $\unicode[STIX]{x1D706}^{++}$ -Souslin tree.

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This research was partially supported by the Israel Science Foundation (grant #1630/14).

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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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