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arXiv · 1708.06932

A forcing axiom deciding the generalized Souslin Hypothesis

Chris Lambie-Hanson·Assaf Rinot
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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 $λ$, if $λ^{++}$ is not a Mahlo cardinal in Gödel's constructible universe, then $2^λ= λ^+$ entails the existence of a $λ^+$-complete $λ^{++}$-Souslin tree.

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BibTeXRIS

Chris Lambie-Hanson, Assaf Rinot. 2018-09-22. A forcing axiom deciding the generalized Souslin Hypothesis. https://doi.org/10.4153/cjm-2017-058-2

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