## Journal of Symbolic Logic

### Strictly Primitive Recursive Realizability, I

Zlatan Damnjanovic

#### 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 $\Sigma^0_1$ formulae is proved. A dual concept of falsifiability is proposed and an analogous soundness result is established for a further restricted fragment of HA.

#### Article information

Source
J. Symbolic Logic, Volume 59, Issue 4 (1994), 1210-1227.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183744620

Mathematical Reviews number (MathSciNet)
MR1312305

Zentralblatt MATH identifier
0816.03029

JSTOR
• 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.