User blog comment:Ytosk/Trying to define Bowers' K(n) systems/@comment-43798125-20191031221625/@comment-38817512-20191101071352

By axiomatic system i mean a set of formulae, which can contain quantifiers(for all, exists), binary logical connectives(and, or, ⇔, ⇒), the symbol ¬, variables, function symbols and relation symbols. The formulae are formed by these rules:

A variable is a term.

For terms x1, x2, x3, ... xn, and a function symbol f, f(x1,x2,x3,...,xn) is a term.

For terms x1, x2, x3, ... xn and a relation symbol r, r(x1,x2,x3,...,xn) is a formula.

For formulae p, q, and a binary logical connective l, plq is a formula.

For a formula p, ¬p is a formula

For a variable x, a quantifier a, and a formula p, ax(p) is a formula.