We consider different characterizations of computability by means of infinite time Blum–Shub–Smale machines (ITBM) via specific functions on sets and computable infinitary formulas.
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P. Koepke and A.Morozov, “Characterizations of ITBM-computability. II,” Algebra and Logic, 59, No. 6, 423-436 (2020).
P. Koepke and A. Morozov, “The computational power of infinite time Blum–Shub–Smale machines,” Algebra and Logic, 56, No. 1, 37-62 (2017).
G. E. Sacks, Higher Recursion Theory (Perspect. Math. Log.), Springer, Berlin (1990).
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P. Koepke and A. S. Morozov are supported by the Alexander von Humboldt Foundation. The results were obtained during the second author’s visit to the University of Bonn in spring 2017.
Translated from Algebra i Logika, Vol. 60, No. 1, pp. 39-56, January-February, 2021. https://doi.org/10.33048/alglog.2021.60.103
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Koepke, P., Morozov, A.S. Characterizations of ITBM-Computability. II. Algebra Logic 60, 26–37 (2021). https://doi.org/10.1007/s10469-021-09625-z
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DOI: https://doi.org/10.1007/s10469-021-09625-z