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Abstract: 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 of simultaneous reflection follows from the Set Mapping Reflection Principle, a consequence of PFA. While the results fall short of showing that MRP implies SCH, it will be shown that MRP implies that if SCH fails first at then every stationary subset of reflects. It will also be demonstrated that MRP always fails in a generic extension by Prikry forcing. [Copyright &y& Elsevier]

We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses the reflection principle MRP introduced by Moore in [11]. [ABSTRACT FROM AUTHOR]