Provably total functions of Basic Arithemtic

Mathematical Logic Quarterly 49 (3):316 (2003)
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Abstract

It is shown that all the provably total functions of Basic Arithmetic BA, a theory introduced by Ruitenburg based on Predicate Basic Calculus, are primitive recursive. Along the proof a new kind of primitive recursive realizability to which BA is sound, is introduced. This realizability is similar to Kleene's recursive realizability, except that recursive functions are restricted to primitive recursives

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Saeed Salehi
University of Tabriz

Citations of this work

Polynomially Bounded Recursive Realizability.Saeed Salehi - 2005 - Notre Dame Journal of Formal Logic 46 (4):407-417.

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References found in this work

Basic Propositional Calculus I.Mohammad Ardeshir & Wim Ruitenburg - 1998 - Mathematical Logic Quarterly 44 (3):317-343.
Fragments of $HA$ based on $\Sigma_1$ -induction.Kai F. Wehmeier - 1997 - Archive for Mathematical Logic 37 (1):37-49.
Basic Predicate Calculus.Wim Ruitenburg - 1998 - Notre Dame Journal of Formal Logic 39 (1):18-46.

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