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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

Robert A. Di Paola
The Journal of Symbolic Logic
Vol. 46, No. 2 (Jun., 1981), pp. 216-232
DOI: 10.2307/2273615
Stable URL: http://www.jstor.org/stable/2273615
Page Count: 17
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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
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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 $\lambda < \alpha^\ast$, 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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