Strictly primitive recursive realizability, I

Journal of Symbolic Logic 59 (4):1210-1227 (1994)
Abstract
A realizability notion that employs only primitive recursive functions is defined, and, relative to it, the soundness of the fragment of Heyting Arithmetic (HA) in which induction is restricted to Σ 0 1 formulae is proved. A dual concept of falsifiability is proposed and an analogous soundness result is established for a further restricted fragment of HA
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DOI 10.2307/2275700
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References found in this work BETA
Enumeration and the Grzegorczyk Hierarchy.Paul Axt - 1963 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (1-4):53-65.
Equivalence of Some Hierarchies of Primitive Recursive Functions.Keith Harrow - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):411-418.
Enumeration and the Grzegorczyk Hierarchy.Paul Axt - 1963 - Mathematical Logic Quarterly 9 (1‐4):53-65.
Equivalence of Some Hierarchies of Primitive Recursive Functions.Keith Harrow - 1979 - Mathematical Logic Quarterly 25 (25‐29):411-418.

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Citations of this work BETA
Elementary Realizability.Zlatan Damnjanovic - 1997 - Journal of Philosophical Logic 26 (3):311-339.

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