  An  L-formula  is called a Δ0-formula if it is equivalent to a formula in which all quantifiers are of the form ∀x∈y or ∃x∈y (i.e., ∀x(x∈y → …) or ∃x(x∈y  ∧  …)). An  L-formula  is a Σ1-formula if it is equivalent to one which can be built up from atomic formulas and their negations using only the logical operators  ∧,   ∨, ∀x∈y, ∃x. A subset X of a set A is said to be Δ0 (resp. Σ1) on A if it is definable in the structure ⟨A, ∈ ⨡ A⟩ by a Δ0- (resp. Σ1-) formula of  L.