The head axiom. In section 2.1.1, I defined headedness as a cumulative property of an element. Unlike derivational and interpretable properties, the presence of the head property on an element does not impose any restrictions on the other properties of that element. Nevertheless, the distribution of heads is still governed by a single axiom, which applies to all phonological heads in the theory. I define it as follows: Axiom VI (unique headedness). A head defines a unique element among a set of elements with the same interpretable properties connected by a binary relation ℛ. (xvi) Head elements are parasitic on another heterogeneous binary relation (dominance or correspondence). The relation defines a field where the head operates. In other words, a head is always a head of a set of elements, a field, which is defined by a binary relation. This definition is commonly assumed in definitions of headedness in the literature. Let us consider prosodic heads as an example. A head foot is a foot that is a head of the domain defined by the dominance relation of its dominating node (let us say, the prosodic word). Its status as head is defined with respect to other feet that are non-heads and that are dominated by the same node (i.e., are in the same domain). The same goes with syllables. A head syllable exists as a special syllable in the domain defined by all the syllables dominated by the same foot. There cannot be two head feet dominated by the same prosodic word (i.e., two primary stresses), and there cannot be two head syllables dominated by the same foot. In the case of φ-Correspondence, the field is defined by correspondence relations. In particular, a φ-head is the head of a correspondence field, which is defined by the set of elements in φ-correspondence. In (14), the head •3 is the head of the field {•2, •3}[+sib] defined by the correspondence relation ℛ[+sib] = {{⟨•3, •1⟩, {⟨•3, •2⟩}.
