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December 2007 An untyped higher order logic with Y combinator
James H. Andrews
J. Symbolic Logic 72(4): 1385-1404 (December 2007). DOI: 10.2178/jsl/1203350794

Abstract

We define a higher order logic which has only a notion of sort rather than a notion of type, and which permits all terms of the untyped lambda calculus and allows the use of the Y combinator in writing recursive predicates. The consistency of the logic is maintained by a distinction between use and mention, as in Gilmore’s logics. We give a consistent model theory, a proof system which is sound with respect to the model theory, and a cut-elimination proof for the proof system. We also give examples showing what formulas can and cannot be used in the logic.

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James H. Andrews. "An untyped higher order logic with Y combinator." J. Symbolic Logic 72 (4) 1385 - 1404, December 2007. https://doi.org/10.2178/jsl/1203350794

Information

Published: December 2007
First available in Project Euclid: 18 February 2008

zbMATH: 1134.03010
MathSciNet: MR2371213
Digital Object Identifier: 10.2178/jsl/1203350794

Rights: Copyright © 2007 Association for Symbolic Logic

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Vol.72 • No. 4 • December 2007
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