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Statman's 1-Section Theorem  is an important but little-known result in the model theory of the simply-typed λ-calculus. The λ-Section Theorem states a necessary and sufficient condition on models of the simply-typed λ-calculus for determining whether βη-equational reasoning is complete for proving equations that hold in a model. We review the statement of the theorem, give a detailed proof, and discuss its significance.
Jon G. Riecke, "Statman's 1-Section Theorem", . January 1992.
Date Posted: 08 August 2007