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A forcing axiom deciding the generalized Souslin Hypothesis

  • Chris Lambie-Hanson,
    Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
  • Assaf Rinot,
    Department of Mathematics, Bar-Ilan University, Ramat-Gan 5290002, Israel
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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 $\lambda$, if $\lambda^{++}$ is not a Mahlo cardinal in Gödel's constructible universe, then $2^\lambda = \lambda^+$ entails the existence of a $\lambda^+$-complete $\lambda^{++}$-Souslin tree.
Keywords: Souslin tree, square, diamond, sharply dense set, forcing axiom, SDFA Souslin tree, square, diamond, sharply dense set, forcing axiom, SDFA
MSC Classifications: 03E05, 03E35, 03E57 show english descriptions Other combinatorial set theory
Consistency and independence results
Generic absoluteness and forcing axioms [See also 03E50]
03E05 - Other combinatorial set theory
03E35 - Consistency and independence results
03E57 - Generic absoluteness and forcing axioms [See also 03E50]
 

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