Usuba's principle $UB_\lambda$ can fail at singular cardinals
Mohammad Golshani, Saharon Shelah
TL;DR
This paper demonstrates that Usuba's combinatorial principle $UB__$ can fail at singular cardinals, including the specific case of leph_ _, providing a counterexample to previous assumptions.
Contribution
It shows that $UB__$ can fail at singular cardinals, addressing a question posed by Usuba and expanding understanding of combinatorial principles at such cardinals.
Findings
$UB__$ can fail at leph_ _.
Failure occurs at leph_ _, including leph_ _.
Provides a counterexample to previous beliefs about $UB__$ at singular cardinals.
Abstract
We answer a question of Usuba by showing that the combinatorial principle can fail at a singular cardinal. Furthermore, can be taken to be
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Taxonomy
TopicsAdvanced Topology and Set Theory · Algebraic Geometry and Number Theory · Computability, Logic, AI Algorithms