The purpose of this paper is to present some results which suggest that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. What will be proved is that a form ...
We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses the reflection principle MRP introduced by Moore in [11].
We determine exact consistency strengths for various failures of the Singular Cardinals Hypothesis (SCH) in the setting of the Zermelo-Fraenkel axiom system ZF without the Axiom o...