Notre Dame Journal of Formal Logic

On Gabbay's Proof of the Craig Interpolation Theorem for Intuitionistic Predicate Logic

Michael Makkai


Using the framework of categorical logic, this paper analyzes and streamlines Gabbay's semantical proof of the Craig interpolation theorem for intuitionistic predicate logic. In the process, an apparently new and interesting fact about the relation of coherent and intuitionistic logic is found.

Article information

Notre Dame J. Formal Logic, Volume 36, Number 3 (1995), 364-381.

First available in Project Euclid: 17 December 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03G30: Categorical logic, topoi [See also 18B25, 18C05, 18C10]
Secondary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03C40: Interpolation, preservation, definability 03F55: Intuitionistic mathematics


Makkai, Michael. On Gabbay's Proof of the Craig Interpolation Theorem for Intuitionistic Predicate Logic. Notre Dame J. Formal Logic 36 (1995), no. 3, 364--381. doi:10.1305/ndjfl/1040149353.

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