A forcing axiom deciding the generalized Souslin Hypothesis

DOI10.4153/CJM-2017-058-2arXiv1708.06932WikidataQ113999192 ScholiaQ113999192MaRDI QIDQ6290416

Assaf Rinot, Chris Lambie-Hanson

Publication date: 23 August 2017

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 $lambd{a}^{++}$ is not a Mahlo cardinal in G"odel's constructible universe, then $2^{l}ambda=lambd{a}^{+}$ entails the existence of a $lambd{a}^{+}$-complete $lambd{a}^{++}$-Souslin tree.

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Other combinatorial set theory (03E05) Generic absoluteness and forcing axioms (03E57)

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