\b[No.] The <prime-sign automorphism of the multiplicative integers> from the preceding part sends the positive integer two to minus two. It therefore does not preserve the nonnegative integers, contradicting the necessary <automorphism invariance of parameter-free definability>. This also excludes definability of the strictly positive integers if that convention for the printed notation is used.

Solution

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

 Solution (source code)