3 papers
math.LO2025
On Shelah's Approachability Ideal
Hannes Jakob, Alejandro Poveda
We solve a long-standing open problem of Shelah regarding the \emph{Approachability Ideal} . Given a singular cardinal , a regular cardinal $μ\in (\mathrm{cf}(γ),…
math.LO2025
Failure of Approachability at the Successor of the first Singular for any Cofinality
Hannes Jakob, Maxwell Levine
We solve two long-standing open problems regarding the combinatorics of . We answer a question of Shelah by showing that it is consistent for any that $\mat…
math.LO2024
On Friedman's Property
Hannes Jakob
We define forcing orders which add witnesses to the failure of various forms of Friedman's Property. These posets behave similarly to the forcing order adding a nonreflecting stati…