9 papers · 1 filter
A Topological Rainbow Ramsey Theorem
Hannes Jakob, Jing Zhang
We show that it is consistent relative to the existence of suitable large cardinals that for any countable-to-one coloring , there exists a closed subset $A\subs…
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),…
Total Failure of Approachability at Successors of Singulars of Countable Cofinality
Hannes Jakob
Relative to class many supercompact cardinals, we construct a model of $\ZFC+\GCH$ where for every singular cardinal of countable cofinality and every regular uncountable …
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…
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…
Distinguishing Internally Club and Approachable on an Infinite Interval
Hannes Jakob, Maxwell Levine
Krueger showed that PFA implies that for all regular , there are stationarily many that are internally club but not internally approachable. From…