Recursion theory and the lambda-calculus

Abstract

AbstractA 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 gödel numbers for partial recursive functions in two standard ω-URS's 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.