Before revision: Definitions A theory of first-order logic is geometric if it is can be axiomatised using only axioms of the form where I and J are disjoint collections of formulae indices that each may be infinite and the formulae φ are either atoms or negations of atoms.
After revision:  where I and J are disjoint collections of formulae indices that each may be infinite and the formulae φ are either atoms or negations of atoms.