That is, it formalizes the concept that is normally expressed by saying that a sentence, statement or idea "is true."
Based on "Chomsky Definition", a language is assumed to be a countable set of sentences, each of finite length, and constructed out of a countable set of symbols.
A theory of syntax is assumed to introduce symbols, and rules to construct well-formed sentences.
A language is called fully interpreted if meanings are attached to its sentences so that they all are either true or false.
The main tools to prove this result are ordinary and transfinite induction, recursion methods, and ZF set theory (cf.