| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4662533 | Annals of Pure and Applied Logic | 2006 | 5 Pages |
Abstract
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 κ then every stationary subset of reflects. It will also be demonstrated that MRP always fails in a generic extension by Prikry forcing.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
