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A lift of a theorem of Friedberg: A Banach-Mazur functional that coincides with no α-recursive functional on the class of α-recursive functions

Published online by Cambridge University Press:  12 March 2014

Robert A. di Paola
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Abstract

R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that λ < α*, where α* is the Σ1-projectum of α and λ is the Σ2-cofinality of α. The theorem is also established for the metarecursive case, α = ω1, where α* = λ = ω.

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 2 , June 1981 , pp. 216 - 232
Copyright
Copyright © Association for Symbolic Logic 1981

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References

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