“School of Mathematics”
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Paper IPM / M / 2321  


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
of 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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