Square principles in Pmax extensions

Abstract

By forcing with ${\mathbb{P}}_{\max }$ over strong models of determinacy, we obtain models where different square principles at ${\omega }_2$ and ${\omega }_3$ fail. In particular, we obtain a model of $2^{{\aleph }_0}=2^{{\aleph }_1}={\aleph }_2+\neg \square ({\omega }_2)+\neg \square ({\omega }_3)$.

Revised version, incorporating the referee's suggestions

Cited by in corpus (2)

• A model of the Axiom of Determinacy in which every set of reals is universally Baire
• The exact strength of generic absoluteness for the universally Baire sets