The Maximality of the Typed Lambda Calculus and of Cartesian Closed Categories
arXiv:math/9911073
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.
21 pages, published in Publications de l'Institut Mathematique, note with additional reference added in September 2012