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December 2012 The range property fails for H
Andrew Polonsky
J. Symbolic Logic 77(4): 1195-1210 (December 2012). DOI: 10.2178/jsl.7704080

Abstract

We work in $\lambda{\mathcal{H}}$, the untyped $\lambda$-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 $\lambda$-term $\Xi$ such that $\Xi M=\Xi {\mathtt I} \iff \Xi M\neq \Xi \Omega$. The construction generalizes to ranges of any finite size, and to some other sensible lambda theories.

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Andrew Polonsky. "The range property fails for H." J. Symbolic Logic 77 (4) 1195 - 1210, December 2012. https://doi.org/10.2178/jsl.7704080

Information

Published: December 2012
First available in Project Euclid: 15 October 2012

zbMATH: 1294.03017
MathSciNet: MR3051621
Digital Object Identifier: 10.2178/jsl.7704080

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 4 • December 2012
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