Statman's 1-Section Theorem

Statman?s 1-Section Theorem (Statman, 1985a, in "Harvey Friedman?s Research on the Foundations of Mathematics" ( L. Harrington et al., Eds.), pp. 331-338, North-Holland, Amsterdam) is an important but little-known result in the model theory of the simply typed ?-calculus. The 1-Section Theorem states a necessary and sufficient condition on models of the simply-typed ?-calculus for determining whether s?-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.

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