On the Herbrand functional interpretation

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 interpret...

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Bibliographic Details
Published in:Mathematical logic quarterly 2020-03, Vol.66 (1), p.91-98
Main Authors: Oliva, Paulo, Xu, Chuangjie
Format: Article
Language:English
Subjects:
Dinosaurs
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Summary: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.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.201900067