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APAL
2006

The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis

13 years 11 months ago
The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis
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 then every stationary subset of S + = { < + : cf() = } reflects. It will also be demonstrated that MRP always fails in a generic extension by Prikry forcing.
Justin Tatch Moore
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where APAL
Authors Justin Tatch Moore
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