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The Journal of Symbolic Logic The Journal of Symbolic Logic

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Elementary differences between the (2p)-C. E. and the (2p +1)-c. e. enumeration degrees

Published online by Cambridge University Press:  12 March 2014

I. S. Kalimullin
I. S. Kalimullin
Affiliation:
N.G. Chebotarev Research Institute of Mechanics and, Mathematics Kazan State University, Universitetskaya St. 17, Kazan. 420008, Russia. E-mail: Iskander.Kalimullin@hsu.ru
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E-mail address:
Iskander.Kalimullin@hsu.ru
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Abstract

It is proved that the (2p)-c. e. e-degrees are not elementarily equivalent to the (2p + 1)-c. e. e-degrees for each nonzero p ∈ ω. It follows that m-c. e. e-degrees are not elementarily equivalent to the n-c e. e-degrees if 1 <m < n.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 1 , March 2007 , pp. 277 - 284
Copyright
Copyright © Association for Symbolic Logic 2007

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References

[1]Cooper, S. B., Enumeration reducibility, nondeterministic computations and relative computability of partial functions, Recursion Theory Week, Oberwolfach 1989 (Ambos-Spies, K., Müller, G., and Sacks, G. E., editors), Lecture Notes in Mathematics, vol. 1432, Springer, 1990, pp. 57–110.Google Scholar
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[4]Kalimullin, I. S., Definability of the jump operator in the enumeration degrees, Journal of Mathematical Logic, vol. 3 (2003), no. 2, pp. 257–267.CrossRefGoogle Scholar
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