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Second Order Arithmetic and Pulsating Hierarchies

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Abstract

We implement the machine-oracle modeling of second order arithmetic by means of the iterated Kleene computability. The sought oracle is constructed by using a pulsating transfinite process which is a modification of a similar process used by N. V. Belyakin for solving a particular instance of this problem.

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References

  1. Ganov V. A. and Belyakin N. V., General Theory of Calculations with Oracles [in Russian], Inst. Mat. (Novosibirsk), Novosibirsk (1989).

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  2. Belyakin N. V., “Iterated Kleene computability,” Sibirsk. Mat. Zh., 30, no. 6, 27–32 (1989).

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  3. Belyakin N. V., “Pulsating hierarchies,” Sibirsk. Mat. Zh., 35, no. 3, 520–526 (1994).

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  4. Rogers H., Theory of Recursive Functions and Effective Computability [Russian translation], Mir, Moscow (1972).

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  5. Belyakin N. V., “Generalized calculations and the second-order arithmetic,” Algebra i Logika, 9, no. 4, 375–405 (1970).

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Authors and Affiliations

  1. Novosibirsk State University, Russia

    E. V. Gailit

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  1. E. V. Gailit
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Gailit, E.V. Second Order Arithmetic and Pulsating Hierarchies. Siberian Mathematical Journal 43, 22–27 (2001). https://doi.org/10.1023/A:1013812202344

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  • DOI: https://doi.org/10.1023/A:1013812202344

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