\b[No.] Interpreting the printed $\mathbb Z^{\geqslant}$ as the nonnegative integers, negation is an additive <structure automorphism> carrying the positive integer one outside that set. The set is therefore not invariant under <structure automorphisms> and cannot have <parameter-free definability>. The same argument would apply if the notation were taken to mean the strictly positive integers.

Solution

Past exam of the model theory course of the University of Oxford / 2011 / 1 / b / i / δ / Solution

 Solution (source code)