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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 HAAuthor's Profile
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Citations of this work
Provably total functions of Basic Arithemtic.Saeed Salehi - 2003 - Mathematical Logic Quarterly 49 (3):316.
Polynomially Bounded Recursive Realizability.Saeed Salehi - 2005 - Notre Dame Journal of Formal Logic 46 (4):407-417.
Strictly Primitive Recursive Realizability, II. Completeness with Respect to Iterated Reflection and a Primitive Recursive $\omega$ -Rule.Zlatan Damnjanovic - 1998 - Notre Dame Journal of Formal Logic 39 (3):363-388.
References found in this work
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.
Equivalence of some Hierarchies of Primitive Recursive Functions.Keith Harrow - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):411-418.
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