Square principles in Pmax extensions

Abstract

By forcing with $\mathbb{P}_{\rm max}$ 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 $2^{\aleph_0}=2^{\aleph_1}=\aleph_2 + \lnot\square(\omega_2) + \lnot\square(\omega_3)$.