An invariance notion in recursion theory

An invariance notion in recursion theory

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 part...

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Veröffentlicht in:The Journal of symbolic logic 1982-03, Vol.47 (1), p.48-66
1. Verfasser: Byerly, Robert E.
Format: Artikel
Sprache:eng
Schlagworte:
Arithmetic
Automorphisms
Descendants
Infinite sets
Logical theorems
Mathematical functions
Mathematical theorems
Recursion
Recursion theory
Recursive functions
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Zusammenfassung: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.
ISSN:0022-4812
1943-5886
DOI:10.2307/2273381