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A relativization mechanism in recursion categories

  • Stefano Stefani (a1)

Extract

The study of recursion categories was introduced in [DH] to carry out an algebraic and intrinsic investigation of structures and phenomena which arise in the classical recursion theory. In this paper a recursion categorical arrangement is proposed for some of the concepts of reduction and relativization which are commonplace in studying classical recursive functions and operators. Indeed, this introduction can be done in a natural way, using categorical concepts already defined, without resorting to special structures. In developing the subject outlined one also has the opportunity of discussing the concept of uniform proof in the context of the recursion categories.

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[DH]Di Paola, R. A. and Heller, A., Dominical categories: recursion theory without elements, this Journal, vol. 52 (1987), pp. 594635.
[HE]Heller, A., An existence theorem for recursion categories, this Journal, vol. 55 (1990), pp. 12521268.
[MS]Montagna, F. and Sorbi, A., Creativeness and completeness in categories of partial recursive operators, this Journal, vol. 54 (1989), pp. 10231041.
[ME]Medvedev, Ju. T., Degrees of difficulty of the mass problems, Doklady Akademii Nauk SSSR, vol. 104 (1955), pp. 501504.
[RO]Rogers, H. Jr, Theory of recursive function and effective computability, McGraw-Hill, New York, 1967.
[ROS]Rosolini, G., Continuity and effectiveness in topoi, Ph.D. thesis, Oxford University, Oxford, 1986.
[SO]Sorbi, A., Comparing of the Baire space by means of general recursive operators, Fundamenta Mathematicae, vol. 138 (1991), pp. 112.
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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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