The range property fails for H
Andrew Polonsky · Journal of Symbolic Logic · 2012
Abstract We work in , the untypedλ-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 aλ-term Ξ such that ΞM= ΞI ⇔ ΞM≠ ΞΩ. The construction generalizes to ranges of any finite size, and to some other sensible lambda theories.