  We define a model of predicate logic in which every term and predicate, open
or closed, has an absolute denotation independently of a valuation of the
variables. For each variable a, the domain of the model contains an element
[[a]] which is the denotation of the term a (which is also a variable symbol).
Similarly, the algebra interpreting predicates in the model directly interprets
open predicates. Because of this models must also incorporate notions of
substitution and quantification. These notions are axiomatic, and need not be
applied only to sets of syntax. We prove soundness and show how every
'ordinary' model (i.e. model based on sets and valuations) can be translated to
one of our nominal models, and thus also prove completeness.
