Journal of Symbolic Logic

An untyped higher order logic with Y combinator

James H. Andrews

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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.

Article information

Source
J. Symbolic Logic Volume 72, Issue 4 (2007), 1385-1404.

Dates
First available: 18 February 2008

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1203350794

Digital Object Identifier
doi:10.2178/jsl/1203350794

Mathematical Reviews number (MathSciNet)
MR2371213

Zentralblatt MATH identifier
1134.03010

Citation

Andrews, James H. An untyped higher order logic with Y combinator. Journal of Symbolic Logic 72 (2007), no. 4, 1385--1404. doi:10.2178/jsl/1203350794. http://projecteuclid.org/euclid.jsl/1203350794.


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