Consider the following variant of the Lévy hierarchy on formulas : let $\Phi$ be the set of all meaningful formulas on the alphabet $\in,=,\vee,\wedge,(,),\neg,\exists,\forall$ and a countable set of variables $x_1,x_2, \ldots$. Let $\Sigma_0=\Pi_0$ consists of all formulas in $\Phi$ without quantifiers at all (in the usual Lévy hierarchy, we would replace this with bounded quantifiers), and by induction, let $\Sigma_n$ be the set of formulas of the form $\exists t_1 \exists t_2 \ldots \exists t_r \psi$ where $\psi$ is in $\Pi_{n-1}$, and let $\Pi_n$ be the set of formulas of the form $\forall t_1 \forall t_2 \ldots \forall t_r \psi$ where $\psi$ is in $\Sigma_{n-1}$.
Now let $\Delta$ be the set of sentences that are equivalent to some $\Sigma_1$ formula and equivalent also to some $\Pi_1$ formula at the same time (here "equivalent" means provably equivalent : I say that $\phi$ is equivalent to $\psi$ when $\phi \Leftrightarrow \psi$ is a theorem of ZFC). For example, if $\phi$ is an universally false sentence (i.e. $\neg \phi$ is a theorem of ZFC), we have $\phi \Leftrightarrow \exists x\ (x \neq x)$ and $\phi \Leftrightarrow \forall x\ (x \neq x)$, so that $\phi$ is in $\Delta_1$. Are there other sentences in $\Delta_1$ besides the universally true or universally false ones?