A Forcing Axiom Deciding the Generalized Souslin Hypothesis

Lambie-Hanson, Chris ; Rinot, Assaf

Canadian journal of mathematics, Tome 71 (2019) no. 2, pp. 437-470

Résumé

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.

Détail

DOI : 10.4153/CJM-2017-058-2

Mots-clés : Souslin tree, square, diamond, sharply dense set, forcing axiom, SDFA

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