1. SET MAPPING REFLECTION.
- Author
-
MOORE, JUSTIN TATCH
- Subjects
- *
AXIOMS , *MATHEMATICAL logic , *SET theory , *AXIOMATIC set theory , *MATHEMATICAL continuum , *MARTIN'S axiom , *CONTINUITY - 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 2ω = ω2 and that $L({\mathscr{P}}(\omega_1))$ satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that □(κ) fails for all regular κ > ω1. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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