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Abstract hierarchies and degrees

  • Ljubomir L. Ivanov (a1)


The aim of this paper is to enrich the algebraic-axiomatic approach to recursion theory developed in [1] by an analogue to the classical arithmetical hierarchy and an abstract notion of degree. The results presented here are rather initial and elementary; indeed, the main problem was the very choice of right abstract concepts.



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[1]Ivanov, L. L., Algebraic recursion theory, Ellis Horwood, Chichester, and Halsted Press, New York, 1986.
[2]Ivanov, L. L., Abstract primitive recursiveness does not increase degrees (in preparation).
[3]Kechris, A. S. and Moschovakis, Y. N., Recursion in higher types, Handbook of mathematical logic (Barwise, J., editor), North-Holland, Amsterdam, 1977, pp. 681737.
[4]Moschovakis, Y. N., Abstract first order computability. I, II, Transactions of the American Mathematical Society, vol. 138 (1969), pp. 427–464, 465504.
[5]Moschovakis, Y. N., On the basic notions in the theory of induction, Logic, foundations of mathematics and computability theory (proceedings of the fifth international congress of logic, methodology and philosophy of science, London, Ontario, 1975; Butts, R. E. and Hintikka, J., editors), Reidel, Dordrecht, 1977, pp. 207236.

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Abstract hierarchies and degrees

  • Ljubomir L. Ivanov (a1)


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