On the construction of fully interpreted formal languages which posses their truth predicates
We shall first construct by ordinary recursion method subsets to the set $D$ of G\"odel numbers of the sentences of a language $\mathcal L$. That language is formed by the sentences of a fully interpreted formal language $L$, called an MA language, and sentences containing a monadic predicate letter $T$. From the class of the constructed subsets of $D$ we extract one set $U$ by transfinite recursion method.
Interpret those sentences whose G\"odel numbers are in $U$ as true, and their negations as false. These sentences together form an
MA language. It is a sublanguage of $\mathcal L$ having $L$ as its sublanguage, and $T$ is its truth predicate.