ANEW RELATION-COMBINING THEOREM AND ITS APPLICATION

Let ?ⁿ denote the set of all formulas ?x₁…?x_nP(x₁, …,x_n) = 0], where P is a polynomial with integer coefficients. We prove a new relation-combining theorem from which it follows that if ?ⁿ is undecidable over N, then ?²ⁿ⁺² is undecidable over Z.