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 κ then every stationary subset of S κ + ω = { α < κ + : cf ( α ) = ω } reflects. It will also be demonstrated that MRP always fails in a generic extension by Prikry forcing.
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