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    Mazzanti, Stefano 2013. Iteration on notation and unary functions. Mathematical Logic Quarterly, Vol. 59, Issue. 6, p. 415.


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Unary primitive recursive functions

  • Daniel E. Severin (a1)
  • DOI: http://dx.doi.org/10.2178/jsl/1230396909
  • Published online: 01 March 2014
Abstract
Abstract

In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets.

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[1]Paul Axt , Iteration of relative primitive recursion, Mathematische Annalen, vol. 167 (1966), pp. 5355.

[3]Nadejda Georoieva , Another simplification of the recursion scheme, Archiv für Mathematische Logik, vol. 18 (1976), pp. 13.

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[10]Stefano Mazzanti , Bounded iteration and unary functions, MLQ Mathematical Logic Quarterly, vol. 51 (2005), pp. 8994.

[11]Jovan Naumović , A classification of the one-argument primitive recursive functions, Archiv für Mathematische Logik, vol. 23 (1983), pp. 161174.

[12]Robert W. Ritchie , Classes of recursive functions based on Ackermann's function, Pacific Journal of Mathematics, vol. 15 (1965). no. 3, pp. 10271044.

[13]Julia Robinson , General recursive functions, Proceedings of the American Mathematical Society, vol. 1 (1950), no. 6, pp. 703718.

[14]Julia Robinson , A note on primitive recursive functions, Proceedings of the American Mathematical Society, vol. 6 (1955), no. 4, pp. 667670.

[15]Raphael M. Robinson , Primitive recursive functions, Bulletin of the American Mathematical Society, vol. 53 (1947), no. 10, pp. 925942.

[17]István Szalkai , On the algebraic structure of primitive recursive functions, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 31 (1985). pp. 551556.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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