What is the difference between a statement and sentence in mathematical logic? I have seen many (GENERAL, BEGINNER TYPE) definitions, however, the actual meaning of a sentence I have yet to find, that is non-specific to a particular domain. This would be useful since a statement is defined in terms of a sentence and is one of the first concepts I am introduced to.
 A: I would say most texts don't make a difference between the two. In fact: statement, sentence, claim, and proposition are typically all seen as the same thing: something that has a truth-value.
If a text does make a distinction, I suspect it might be between the syntactical expression that we use in order to express a claim, and the claim itself as more of an abstract idea, in much the same ads a number can be expressed in different ways: a numeral is what represent a number. Likewise, one could see a sentence as representing a statement or claim.
A: In some treatments of mathematical logic where quantified variables appear in the formulas of a language, statement may refer to any formula while sentence refers specifically to a formula without free variables (i.e. variables not bound by a quantifier). So a statement may say something about particular objects under an interpretation of the free variables, while a sentence makes a "general" statement independent of the interpretation of free variables (though it may still say something about particular objects which are definable in the language without parameters). However, this is just one convention for the use of the words "statement" and "sentence" and other treatments may use the words differently.
