Monotone normality and nabla products

Roitman's combinatorial principle $\Delta$ is equivalent to monotone normality of the nabla product, $\nabla (\omega +1)^\omega$. If $\{ X_n : n\in \omega\}$ a family metrizable spaces and $\nabla_n X_n$ monotonically normal, then hereditarily paracompact. Hence, if holds box product $\square +1)^\omega$ Large fragments hold in $\mathsf{ZFC}$, yielding large subspaces (\omega+1)^\omega$ that are `really' normal. Countable products which respectively: arbitrary, size $\le \mathfrak{c}$, or separable, normal under $\mathfrak{b}=\mathfrak{d}$, $\mathfrak{d}=\mathfrak{c}$ Model Hypothesis. It consistent independent A(\omega_1)^\omega$ (\omega_1+1)^\omega$ (or paracompact, normal). In $\mathsf{ZFC}$ neither A(\omega_2)^\omega$ nor (\omega_2+1)^\omega$