 A positive formula is a formula which belongs to the smallest class of formulas containing a false statement \(\bot\), all atomic membership and equality formulas and closed under the formation of conjunctions, disjunctions, universal and existential quantifications. A generalized positive formula is obtained if we allow bounded universal and existential quantifications (the additional strength comes from allowing \((\forall x \in A \mid \phi) \equiv \forall x(x \in A \rightarrow \phi)\); bounded existential quantification is positive in any case).