Exercise 16, § 11

For every prime number $p$ there exists a Moriya field of characteristic $p$ such that the set of degrees of algebraic extensions of finite degree of this field is the set $N^*$ of integers $> 0$^1. Show that for every set $P$ of prime numbers, there exists a Moriya field $K$ of any characteristic, such that the set of degrees of algebraic extensions of finite degree of $K$ is the set $N$, (argue as in Ex. 14, b)).