  In the following paper we propose a model-theoretical way of comparing the
"strength" of various truth theories which are conservative over PA.
  Let $\mathfrak{Th}$ denote the class of models of PA which admit an expansion
to a model of theory Th. We show (combining some well known results and
original ideas) that $$\mathfrak{PA}\supset \mathfrak{TB}\supset
\mathfrak{RS}\supset \mathfrak{UTB}\supseteq\mathfrak{CT^-},$$ where
$\mathfrak{PA}$ denotes simply the class of all models of PA and
$\mathfrak{RS}$ denotes the class of recursively saturated models of PA. Our
main original result is that every model of PA which admits an expansion to a
model of CT${}^-$, admits also an expanion to a model of UTB. Moreover, as a
corollary to one of the results we conclude that UTB is not relatively
interpretable in TB, thus answering the question of Fujimoto.
