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math.LO2008
Some consequences of reflection on the approachability ideal
Assaf Sharon, Matteo Viale
We study the approachability ideal I[κ^+] in the context of large cardinals properties of the regular cardinals below a singular κ. As a guiding example consider the approachabilit…
math.LO2007
A family of covering properties for forcing axioms and strongly compact cardinals
Matteo Viale
This paper presents the main results in my Ph.D. thesis. In what follows several proofs of SCH are presented introducing a family of covering properties which implies both SCH and…
math.LO2005
The Proper Forcing Axiom and the Singular Cardinal Hypothesis
Matteo Viale
We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof is by interpolation and uses the Mapping Reflection Principle.