Recursion theory and the lambda-calculus

Journal of Symbolic Logic 47 (1):67-83 (1982)

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 e 1 and e 2 are godel numbers for partial recursive functions in two standard ω-URS's 1 which both act like the same closed lambda-term, then there is an isomorphism of the two ω-URS's which carries e 1 to e 2
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DOI 10.2307/2273382
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References found in this work BETA

Model Theory.Michael Makkai, C. C. Chang & H. J. Keisler - 1991 - Journal of Symbolic Logic 56 (3):1096.
The Calculi of Lambda-Conversion.Alonzo Church - 1941 - Journal of Symbolic Logic 6 (4):171-171.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.

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Effectivizing Inseparability.John Case - 1991 - Mathematical Logic Quarterly 37 (7):97-111.

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