Let ϕ be a fully quantified proposition of predicate logic. Prove that ϕ is logically equivalent to a fully quantified proposition ψ in which all quantifiers are at the outermost level of ψ. In other...

Let ϕ be a fully quantified proposition of predicate logic. Prove that ϕ is logically equivalent to a fully quantified proposition ψ in which all quantifiers are at the outermost level of ψ. In other words, the proposition ψ must be of the form ∀

where each ∀/∃ is either a universal or existential quantifier. (The transformation that you performed in Exercise 3.178 put Goldbach’s Conjecture in this special form.) (Hint: you might find the results from Exercises 4.66–4.71 helpful. Using these results, you can assume that ϕ has a very particular form.)

Exercises 4.66–4.71