Abstract
We continue research on machine-oracle modelling of second-order arithmetic. The pulsating process described in [1, 2] is simulated using oracles of so-called autonomous hierarchies. The outcome is constructing a generalized constructive model for a fragment of second-order arithmetic described in [2].
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REFERENCES
N. V. Belyakin, “Pulsating hierarchies, ” Sib. Mat. Zh., 35, No. 3, 520–526 (1994).
E. V. Gailit, “Second-order arithmetic and pulsating hierarchies, ” Sib. Mat. Zh., 43, No. 1, 33–40 (2002).
V. A. Ganov and N. V. Belyakin, General Theory of Computations with Oracles [in Russian], Institute of Mathematics SO AN SSSR, Novosibirsk (1989).
N. V. Belyakin, “Iterated Kleene computability, ” Sib. Mat. Zh., 30, No. 6, 27–32 (1989).
E. G. Nikiforova, “A method for regulating the iterated Kleene computability, ” Dep. VINITI, No. 2696-B (1988).
N. V. Belyakin, “Effective hierarchies, ” Algebra Logika, 29, No. 4, 385–397 (1990).
A. N. Gamova, “Superautonomous numberings and projected ordinals, ” Algebra Logika, 30, No. 1, 28–47 (1991).
H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).
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Gailit, E.V. Modelling the Pulsating Process. Algebra and Logic 42, 357–364 (2003). https://doi.org/10.1023/B:ALLO.0000004169.60673.90
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DOI: https://doi.org/10.1023/B:ALLO.0000004169.60673.90