We show that the types of the witnesses in the Herbrand functional interpretation can be simplified, avoiding the use of "sets of functionals" in the interpretation of implication and universal quantification. This is done by presenting an alternative formulation of the Herbrand functional interpretation, which we show to be equivalent to the original presentation. As a result of this investigation we also strengthen the monotonicity property of the original presentation, and prove a monotonicity property for our alternative definition.

中文翻译：

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论 Herbrand 的功能解读

我们表明 Herbrand 泛函解释中的证人类型可以简化，避免在蕴涵和全称量化解释中使用“泛函集”。这是通过提出 Herbrand 函数解释的替代公式来完成的，我们证明它与原始表述等效。作为这项调查的结果，我们还加强了原始表示的单调性，并证明了我们替代定义的单调性。