universal relation (original) (raw)

If Φ is a class of n-ary relations with x→ as the only free variables, an n+1-ary formula ψ is universal for Φ if for any ϕ∈Φ there is some e such that ψ⁢(e,x→)↔ϕ⁢(x→). In other words, ψ can simulate any element of Φ.

Similarly, if Φ is a class of function of x→, a formula ψ is universal for Φ if for any ϕ∈Φ there is some e such that ψ⁢(e,x→)=ϕ⁢(x→).