A forcing axiom deciding the generalized Souslin Hypothesis

Joint work with Chris Lambie-Hanson.

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 Godel’s constructible universe, then $2^\lambda = \lambda^+$ entails the existence of a  $\lambda^+$-complete $\lambda^{++}$-Souslin tree.

Downloads:

Citation information:

C. Lambie-Hanson and A. Rinot, A forcing axiom deciding the generalized Souslin Hypothesis, Canad. J. Math., 71(2): 437-470, 2019.

This entry was posted in Publications, Souslin Hypothesis and tagged , , , , , , , . Bookmark the permalink.

One Response to A forcing axiom deciding the generalized Souslin Hypothesis

  1. saf says:

    Submitted to Canad. J. Math., July 2017.
    Accepted, November 2017.

Leave a Reply

Your email address will not be published. Required fields are marked *