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The range property fails for H

Published online by Cambridge University Press:  12 March 2014

Andrew Polonsky
Andrew Polonsky*
Affiliation:
University of Nijmegen, Faculty of Science, Neijendaalseweg 135, 6525AJ Nijmegen, The Netherlands, E-mail: andrew.polonsky@gmail.com
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 4 , December 2012 , pp. 1195 - 1210
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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