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The range property fails for H
Published online by Cambridge University Press: 12 March 2014
Abstract
We work in , the untyped λ-calculus in which all unsolvables are identified. We resolve a conjecture of Barendregt asserting that the range of a definable map is either infinite or a singleton. This is refuted by constructing a λ-term Ξ such that ΞM = ΞI ⇔ ΞM ≠ ΞΩ. The construction generalizes to ranges of any finite size, and to some other sensible lambda theories.
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- Copyright © Association for Symbolic Logic 2012
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