  We recall and refine some definitions from the entries on  classical logic  and  model theory.  A signature is a set of individual constants, predicate symbols and function symbols; each of the predicate symbols and function symbols has an arity (for example it is binary if its arity is 2). Each signature K gives rise to a first-order language, by building up formulas from the symbols in the signature together with logical symbols (including =) and punctuation.