4 papers · 1 filter
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…
Good Scales and Non-Compactness of Squares
Maxwell Levine, Heike Mildenberger
Cummings, Foreman, and Magidor investigated the extent to which square principles are compact at singular cardinals. The first author proved that if is a singular strong limit…
On Namba Forcing and Minimal Collapses
Maxwell Levine
We build on a 1990 paper of Bukovsky and Coplakova-Hartova. First, we remove the hypothesis of from one of their minimality results. Then, using a measurable cardinal…
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…