Set mapping reflection

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 2^omega = omega_2 and that L(P(omega_1)) 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 > omega_1.

11 pages

Cited by in corpus (14)

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• Chang's Conjecture, The Weak Reflection Principle and the Tree Property at ${\omega }_2$
• What model companionship can say about the Continuum problem
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• Definable MAD families and forcing axioms
• Bounded forcing axioms and Baumgartner's conjecture
• Forcing Axioms and the Definabilty of the Nonstationary Ideal on ${\omega }_1$
• Absolute model companionship, forcibility, and the continuum problem
• The model-companionship spectrum of set theory, generic absoluteness, and the Continuum problem
• Bounded Martin's Maximum with Many Witnesses
• The Stationary Set Splitting Game