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An Invariance Notion in Recursion Theory
Robert E. Byerly
The Journal of Symbolic Logic
Vol. 47, No. 1 (Mar., 1982), pp. 48-66
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/2273381
Page Count: 19
You can always find the topics here!Topics: Recursive functions, Automorphisms, Recursion theory, Recursion, Mathematical theorems, Infinite sets, Arithmetic, Descendants, Logical theorems, Mathematical functions
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A set of godel numbers is invariant if it is closed under automorphisms of (ω, ·), where ω is the set of all godel numbers of partial recursive functions and · is application (i.e., n · m ≃ φn(m)). The invariant arithmetic sets are investigated, and the invariant recursively enumerable sets and partial recursive functions are partially characterized.
The Journal of Symbolic Logic © 1982 Association for Symbolic Logic