In "The Semantic Conception of Truth and the Foundations of Semantics" (1944) Alfred Tarski asserts that a satisfactory definition of truth must be both formally correct and materially adequate. A theory of truth is formally correct iff it does not contradict the rules of the language in which it is given (the metalanguage describing the object language). Furthermore, a theory of truth is materially adequate if it entails all the equivalences (T) in the object language of the form "X is true if, and only if, p," where 'p' is an arbitrary sentence in the object language and 'X' is the name of that sentence in the metalanguage.
The definition of truth Tarski finally decides to put forward is "a sentence is true if it is satisfied by all objects, and false otherwise." For example, if snow satisfies the sentence "Snow is white," then the sentence is true. My question is, how can it be shown that this definition of truth is formally correct and that it implies all equivalences (T) in the object language? It may be that the treatment of the theory I am reading is just an outline, or that I am misunderstanding something, but either way it would be of great help if someone could point me in the right direction.