Negating the Galvin Property
Tom Benhamou, Shimon Garti, Alejandro Poveda
TL;DR
This paper demonstrates the consistent failure of Galvin's property at successors of singular cardinals and explores the impact of Prikry-type forcings and large cardinals on this phenomenon.
Contribution
It establishes new consistency results regarding the failure of Galvin's property at certain cardinals and analyzes the influence of Prikry-type forcings and large cardinals.
Findings
Galvin's property can fail at successors of strong limit singular cardinals.
Failure of Galvin's property can be consistent at all successors of singular cardinals.
Prikry-type forcings affect the strong failure of Galvin's 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
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Economic theories and models