The Proper Forcing Axiom and the Singular Cardinal Hypothesis
Journal of Symbolic Logic 71 (2):473 - 479 (2006)
Abstract
We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses the reflection principle MRP introduced by Moore in [11]DOI
10.2178/jsl/1146620153
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Citations of this work
Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
Aronszajn trees, square principles, and stationary reflection.Chris Lambie-Hanson - 2017 - Mathematical Logic Quarterly 63 (3-4):265-281.
Squares and covering matrices.Chris Lambie-Hanson - 2014 - Annals of Pure and Applied Logic 165 (2):673-694.
Simple proofs of $${\mathsf{SCH}}$$ SCH from reflection principles without using better scales.Hiroshi Sakai - 2015 - Archive for Mathematical Logic 54 (5-6):639-647.
References found in this work
Fragments of Martin's Maximum in generic extensions.Y. Yoshinobu & B. Konig - 2004 - Mathematical Logic Quarterly 50 (3):297.
Blowing up power of a singular cardinal—wider gaps.Moti Gitik - 2002 - Annals of Pure and Applied Logic 116 (1-3):1-38.
The proper forcing axiom, Prikry forcing, and the singular cardinals hypothesis.Justin Tatch Moore - 2006 - Annals of Pure and Applied Logic 140 (1):128-132.
