Set Mapping Reflection

In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2ω = ω2 and that satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that □(κ) fails for all regular κ > ω1.

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