For the sake of definiteness we assume that the language of arithmetic has exactly \(\neg , \wedge\) and \(\vee\) as connectives and \(\forall\) and \(\exists\) as quantifiers. It has as individual constants only the symbol 0 for zero; its only function symbol is the unary successor symbol \(S\); addition and multiplication are expressed by predicate symbols. Therefore the only closed terms of the language of arithmetic are the numerals \(0, S\)(0), \(S(S\)(0)), \(S(S(S\)(0))), ….