Strictly primitive recursive realizability, I

Journal of Symbolic Logic 59 (4):1210-1227 (1994)
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
Keith Harrow (1979). Equivalence of Some Hierarchies of Primitive Recursive Functions. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):411-418.
Paul Axt (1963). Enumeration and the Grzegorczyk Hierarchy. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (1-4):53-65.
Paul Axt (1963). Enumeration and the Grzegorczyk Hierarchy. Mathematical Logic Quarterly 9 (1‐4):53-65.

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

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