Tarski's conception of truth In The Semantic Conception of truth: and the Foundations of Semantics, Tarski defines his conception of truth as follows:
“Let us consider an arbitrary sentence; we shall replace it by the letter ‘$p$.’ We form the name of this sentence and we replace it by another letter, say ‘$X$.’ We ask now what is the logical relation between the two sentences ‘$X$ is true’ and ‘$p$.’ It is clear that from the point of view of our basic conception of truth these sentences are equivalent. In other words, the following equivalence holds:
(T) $X$ is true if, and only if, $p$."
Now, let $h:\mathcal{A}\mapsto\mathbf{2}$ be an interpretation from an algebra $\mathcal{A}$ of sentences of a given language to the Boolean algebra $\mathbf{2}$ (the Boolean algebra whose domain is $\{0,1\}$) of the same type.
I have a doubt about what Tarski means by the "name of a sentence". Suppose for example that $p$ is in the algebra $\mathcal{A}$. Does Tarski's schema (T) mean that:
(T) $h(p)$ is true if, and only if, $p$?
Put differently, does the name of a sentence correspond to $h(p)$?
 A: As said by Tarski in the previous page, the prdicate "is true" applies not to sentences but to names of sentences :

from the point of view of the grammar of our language, an expression of the form "$X$ is true" will not become a meaningful sentence if we replace in it '$X$'by a sentence or by anything other than a name.

The usul way is to use quotation marks to transfrom a sentence in its name; thus, the "correct syntax" sugegsted by Tarski is :

"the snow is white" is true iff the snow is white.

The left occurrence of the expression the snow is white (enclosed by quotation marks) is used to refer to an expression of the language (i.e. to name itself) while the right occurrence (not enclosed by quotation marks) is an expression used in its "normal" role : referring to a "fact".

If we are familiar with the technique developed by Gödel : the Gödel Numbering, we can use Gödel Number (or code) $\ulcorner \varphi \urcorner$ as a name for a formula $\varphi$ of the (formal) language.
Thus, Tarski's condition will be :

$\ulcorner \varphi \urcorner$ is true iff $\varphi$.

