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The Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories

Kosta Dosen·Zoran Petric
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Abstract

From the analogue of Boehm's Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies an equality between arrows not satisfied in free cartesian closed categories must be a preorder. A new proof is given here of these results, which were obtained previously by Richard Statman and Alex K. Simpson.

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Kosta Dosen, Zoran Petric. 2012-09-25. The Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories. https://arxiv.org/abs/math/9911073

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