Considering only pure sets, the naive set comprehension principle says, for any condition, that there is a set containing all and only the sets satisfying this condition. In first-order logic, this can be formulated as the following schematic principle, where ϕ may be any formula in whichy does not occur freely: ∃y∀x(x∈y↔ϕ). (1.1)

Russell's paradox shows that the instance obtained by letting ϕ be x∉x is inconsistent in classical logic. One response to the paradox is to restrict naive set comprehension by ruling out this and other problematic instances: only for each of some special conditions is it claimed there is a set containing all and only the sets satisfying the condition. Many well known set theories can be understood as instances of this generic response,differing in how they understand special.For example,the axiom schema of separation (1.1) in Zermelo-Fraenkel set theory (ZF) restricts set comprehension to conditions which contain, as a conjunct, the condition of being a member of some given set: ∃y∀x(x∈y↔ϕ∧x∈z). (1.2) Similarly, in Quine's New Foundations (NF) set comprehension is restricted to conditions which are stratified, where ϕ is stratified just in case there is a mapping f from individual variables to natural numbers such that for each subformula of ϕ of the form x∈ y,f(y)= f(x)+1 and for each subformula of ϕ of the form x=y,f(x)=f(y). Both of these responses block Russell's paradox by ruling out the condition x∉x. Must every restriction of naive comprehension take the form of simply ruling out certain instances? In this article, I have suggest and explore a different approach. As we have seen,standard set comprehension axioms restrict attention to some special conditions: for each of these special conditions, they provide for the existence of a set containing all and only the sets which satisfy it.