I've been reading lately Model Theory of Modal Logic by Otto and Goranko. At one point, I found something like this:
"Let $\varphi$ be a modal formula with modal depth of $n+1$. Propositional connectives in $\varphi$ can be unravelled so that without loss of generality $\varphi$ is of the form $\diamond\psi$ for some $\psi$ with modal depth equal to $n$."
Does anyone know how to prove this?
The modal depth of (◇P ∧ ◇Q) is 1, at least as modal depth is usually defined.
This wff can't be put in the form ◇ψ where ψ is has modal depth zero, i.e. is modality-free.
So the quoted claim looks wrong -- I suspect a mis-statement.