12. When a non-empty set of numbers $F$ satisfies the condition: "If $a, b \in F$, then $a+b, a-b, a \cdot b \in F$, and when $b \neq 0$, $\frac{a}{b} \in F$", we call $F$ a number field. Among the following four propositions about number fields:
(1) 0 is an element of any number field;
(2) If a number field $F$ has a non-zero element, then $2016 \in F$;
(3) The set $P=\{x \mid x=3 k, k \in \mathbf{Z}\}$ is a number field;
(4) The set of rational numbers is a number field.

The true propositions are $\qquad$ (write down the codes of all true propositions).
According to the definition of a number field, (1)(2)(4) are correct.