Negating the Galvin Property

Abstract

We prove that Galvin's property consistently fails at successors of strong limit singular cardinals. We also prove the consistency of this property failing at every successor of a singular cardinal. In addition, the paper analyzes the effect of Prikry-type forcings on the strong failure of the Galvin property and explores stronger forms of this property in the context of large cardinals

References in corpus (10)

• Weak diamond and Galvin's property
• Intermediate Models of Magidor-Radin Forcing- Part II
• Partition Calculus and Cardinal Invariants
• On the consistency of local and global versions of Chang's Conjecture
• Tiltan
• Kurepa trees and the failure of the Galvin property
• Prikry Forcing and Tree Prikry Forcing of Various Filters
• Martin's maximum and the non-stationary ideal
• Weak prediction principles
• Sigma-Prikry forcing I: The Axioms

Cited by in corpus (7)

• On Cohen and Prikry Forcing Notions
• Cofinal types of ultrafilters over measurable cardinals
• The Galvin property under the Ultrapower Axiom
• Non-Galvin Filters
• Galvin's property at large cardinals and an application to partition calculus
• Superclub, splitting, separating statements
• Magidor-like forcing and the cofinality of the Galvin number