Set mapping reflection
Justin Tatch Moore
Abstract
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 2omega = omega2 and that L(P(omega1)) satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that combinatorial principle Square(kappa) fails for all regular kappa > omega1.
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