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Provably Total Functions of Basic Arithmetic

Saeed Salehi, Provably Total Functions of Basic Arithmetic. Mathematical Logic Quarterly 49(3), 316–322, 2003.

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.

BibTeX entry:

@ARTICLE{jSa03a,
  title = {Provably Total Functions of Basic Arithmetic},
  author = {Salehi, Saeed},
  journal = {Mathematical Logic Quarterly},
  volume = {49},
  number = {3},
  pages = {316–322},
  year = {2003},
  keywords = {Provably total functions • Basic Logic • Basic Arithmetic • realizability },
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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