Higher-order semantics and extensionality

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Journal of Symbolic Logic 69 (4):1027-1088 (2004)
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Abstract

In this paper we re-examine the semantics of classical higher-order logic with the purpose of clarifying the role of extensionality. To reach this goal, we distinguish nine classes of higher-order models with respect to various combinations of Boolean extensionality and three forms of functional extensionality. Furthermore, we develop a methodology of abstract consistency methods needed to analyze completeness of higher-order calculi with respect to these model classes

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Christoph Benzmueller
Freie Universität Berlin

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