 The theory that emerges from (i)–(iii) is further developed with additional axioms and definitions. One axiom asserts that if an object encodes a property, it does so necessarily \((xF \to \Box xF).\) So the properties that an object encodes are not relative to any circumstance. Moreover, Zalta supplements his theory of abstract objects with a theory of properties, relations, and propositions. Here we describe only the theory of properties. It is governed by two principles: a comprehension principle for properties and a principle of identity. The comprehension principle asserts that for any condition on objects expressible without encoding subformulas, there is a property \(F\) such that necessarily, an object \(x\) exemplifies \(F\) if and only if \(x\) is such that \(\phi\), i.e., \(\exists F\Box \forall x(Fx \equiv \phi)\), where \(\phi\) has no encoding subformulas and no free \(F\text{s}\). The identity principle asserts that properties \(F\) and \(G\) are identical just in case \(F\) and \(G\) are necessarily encoded by the same objects, i.e., \(F\! =\! G =_\mathit{df} \Box \forall x(xF \equiv xG)\). This principle allows one to assert that there are properties that are necessarily equivalent in the classical sense, i.e., in the sense that \(\Box \forall x(Fx \equiv Gx)\), but which are  distinct.[11] 