# Notation for the set of conjonctions of two adjacent level of the levy hierarchy

Let $$\Sigma_n$$ and $$\Pi_n$$ be two levels of the levy hierarchy. We consider the set of formulas $$\Gamma = \left\{ \phi \wedge \psi, \phi \in \Sigma_n, \psi \in \Pi_n \right\}$$

Is there a common name for such a $$\Gamma$$ ? Something like $$\Sigma_n \cup \Pi_n$$ or $$\Sigma_n \wedge \Pi_n$$ ?

• I doubt there's a standard notation; using $\sum_n\land\Gamma_n$ (with an explanation) seems reasonable May 18 at 12:16

The standard notation is $$\Sigma_n\wedge\Pi_n$$. See for example the top of page $$23$$ in Arnie Miller's paper On the Borel Classification of the Isomorphism Class of a Countable Model.