Journal of Symbolic Logic

Strictly Primitive Recursive Realizability, I

Zlatan Damnjanovic

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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 $\Sigma^0_1$ 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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J. Symbolic Logic, Volume 59, Issue 4 (1994), 1210-1227.

First available in Project Euclid: 6 July 2007

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Damnjanovic, Zlatan. Strictly Primitive Recursive Realizability, I. J. Symbolic Logic 59 (1994), no. 4, 1210--1227.

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See also

  • Part II: Zlatan Damnjanovic. Strictly Primitive Recursive Realizability. II. Completeness with Respect to Iterated Reflection and a Primitive Recursive $\omega$-rule. Notre Dame J. Formal Logic, vol. 39, no. 3 (1974), 363--388.