Geodesic
A Forcing Axiom Deciding the Generalized Souslin Hypothesis
Canadian journal of mathematics, Tome 71 (2019) no. 2, pp. 437-470

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DOI

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.
DOI : 10.4153/CJM-2017-058-2
Mots-clés : Souslin tree, square, diamond, sharply dense set, forcing axiom, SDFA 
Lambie-Hanson, Chris; Rinot, Assaf. A Forcing Axiom Deciding the Generalized Souslin Hypothesis. Canadian journal of mathematics, Tome 71 (2019) no. 2, pp. 437-470. doi: 10.4153/CJM-2017-058-2
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     title = {A {Forcing} {Axiom} {Deciding} the {Generalized} {Souslin} {Hypothesis}},
     journal = {Canadian journal of mathematics},
     pages = {437--470},
     year = {2019},
     volume = {71},
     number = {2},
     doi = {10.4153/CJM-2017-058-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-058-2/}
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