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Recursion Theory and the Lambda-Calculus

Robert E. Byerly
The Journal of Symbolic Logic
Vol. 47, No. 1 (Mar., 1982), pp. 67-83
DOI: 10.2307/2273382
Stable URL: http://www.jstor.org/stable/2273382
Page Count: 17
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Recursion Theory and the Lambda-Calculus
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Abstract

A semantics for the lambda-calculus due to Friedman is used to describe a large and natural class of categorical recursion-theoretic notions. It is shown that if e1 and e2 are godel numbers for partial recursive functions in two standard ω-URS's1 which both act like the same closed lambda-term, then there is an isomorphism of the two ω-URS's which carries e1 to e2.

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