Journal of Symbolic Logic

An untyped higher order logic with Y combinator

James H. Andrews

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

First available in Project Euclid: 18 February 2008

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

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