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Abstract hierarchies and degrees

Published online by Cambridge University Press:  12 March 2014

Ljubomir L. Ivanov
Ljubomir L. Ivanov*
Affiliation:
Faculty of Mathematics, Sofia University, 1126 Sofia, Bulgaria
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 1 , March 1989 , pp. 16 - 25
Copyright
Copyright © Association for Symbolic Logic 1989

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References

REFERENCES

[1]Ivanov, L. L., Algebraic recursion theory, Ellis Horwood, Chichester, and Halsted Press, New York, 1986.Google Scholar
[2]Ivanov, L. L., Abstract primitive recursiveness does not increase degrees (in preparation).Google Scholar
[3]Kechris, A. S. and Moschovakis, Y. N., Recursion in higher types, Handbook of mathematical logic (Barwise, J., editor), North-Holland, Amsterdam, 1977, pp. 681–737.CrossRefGoogle Scholar
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