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Strictly Primitive Recursive Realizability, I

Zlatan Damnjanovic
The Journal of Symbolic Logic
Vol. 59, No. 4 (Dec., 1994), pp. 1210-1227
DOI: 10.2307/2275700
Stable URL: http://www.jstor.org/stable/2275700
Page Count: 18
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Strictly Primitive Recursive Realizability, I
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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 Σ01 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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