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.

翻译：我们定义了一种谓词逻辑模型，其中每个项和谓词（无论开项或闭项）都具有绝对指称，独立于变量的赋值。对于每个变量a，模型的论域包含一个元素[[a]]，它是项a（同时也是变量符号）的指称。类似地，解释模型中谓词的代数直接解释开谓词。由于这一特性，模型还必须包含替换和量化的概念。这些概念是公理化的，且无需仅应用于语法集合。我们证明了可靠性，并展示了如何将每个“普通”模型（即基于集合和赋值的模型）转换为我们的名词性模型，从而也证明了完备性。