Maxwell Levine

collaborators

3 papers

math.LO2026

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 $I^º$ is a singular strong limit…

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

Classical Namba forcing can have the weak countable approximation property

Maxwell Levine

We show that it is consistent from an inaccessible cardinal that classical Namba forcing has the weak $I ¨ _{1}$ -approximation property. In fact, this is the case if $ℵ_{1}$ -preserv…