 It is standard to extend this syntactic classification of formulas in terms of quantifier complexity to sets and relations on the natural numbers which can be defined by a formula in a given class. Thus, for instance, \(x &lt; y \vee x = y\) is a \(\Delta^0_0\)-formula and the relation \(\leq\) on \(\mathbb{N} \times \mathbb{N}\) is accordingly said to be \(\Delta^0_0\). On the other hand, while \(\exists y(y + y = x)\) is a \(\Sigma^0_1\)-formula, the set of even numbers is also defined by \(\exists y &lt; x(x = 0 \vee y + y = x)\). Thus this set is also classified as \(\Delta^0_0\) in virtue of the existence of this latter definition which is simpler in the sense measured by the arithmetical hierarchy.