  We study the structure of the partial order induced by the definability
relation on definitions of truth for the language of arithmetic. Formally, a
definition of truth is any sentence $\alpha$ which extends a weak arithmetical
theory (which we take to be EA) such that for some formula $\Theta$ and any
arithmetical sentence $\varphi$, $\Theta(\ulcorner\varphi\urcorner)\equiv
\varphi$ is provable in $\alpha$. We say that a sentence $\beta$ is definable
in a sentence $\alpha$, if there exists an unrelativized translation from the
language of $\beta$ to the language of $\alpha$ which is identity on the
arithmetical symbols and such that the translation of $\beta$ is provable in
$\alpha$. Our main result is that the structure consisting of truth definitions
which are conservative over the basic arithmetical theory forms a countable
universal distributive lattice. Additionally, we generalize the result of
Pakhomov and Visser showing that the set of (G\"odel codes of) definitions of
truth is not $\Sigma_2$-definable in the standard model of arithmetic. We
conclude by remarking that no $\Sigma_2$-sentence, satisfying certain further
natural conditions, can be a definition of truth for the language of
arithmetic.
