1 results
A Forcing Axiom Deciding the Generalized Souslin Hypothesis
- Part of
-
- Journal:
- Canadian Journal of Mathematics / Volume 71 / Issue 2 / April 2019
- Published online by Cambridge University Press:
- 07 January 2019, pp. 437-470
- Print publication:
- April 2019
-
- Article
-
- You have access
- Export citation
-
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.
