Hannes Jakob

activity

20242026

collaborators

9 papers

math.LO2026

Cascading Variants of Internal Approachability

Hannes Jakob

We construct models in which there are stationarily many structures that exhibit different variants of internal approachability at different levels. This answers a question of Fore…

math.LO2026

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 $c : [I ¨ _{2}]^{2} \to I ¨ _{2}$ , there exists a closed subset $A\su…

math.LO2026

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 $I^´$ of countable cofinality and every regular uncountable $Î¼<…

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 $ℵ_{I ¨ + 1}$ . We answer a question of Shelah by showing that it is consistent for any $n \geq 1$ that $\ma…

math.LO2025

Slender Trees and the Approximation Property

Hannes Jakob

We obtain a relatively simple criterion for when a forcing has the $< I^´$ -approximation property, generalizing a result of Unger. Afterwards we apply this criterion to construct…

math.LO2025

Disjoint Stationary Sequences on an Interval of Cardinals

Hannes Jakob

We answer a question of Krueger by obtaining -- from countably many Mahlo cardinals -- a model where there is a disjoint stationary sequence on $ℵ_{n + 2}$ for every $n \in I ¨ $ . I…