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Splitting properties of n-c.e. enumeration degrees

  • I. SH. Kalimullin (a1)
Abstract

It is proved that if 1 < m < 2pn for some integer p then the elementary theories of posets of m-c.e. and n-c.e. e-degrees are distinct. It is proved also that the structures 〈2n, ≤, 〉 and 〈2n, ≤. P〉 are not elementary equivalent where P is the predicate P(a) = “a is a e-degree”.

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[1]Ahmad, S., Embedding the diamond in the Σ2 enumeration degrees, this Journal, vol. 50 (1991), pp. 195212.
[2]Arslanov, M. M., Kalimullin, I. Sh., and Sorbi, A., Density results in the Δ20 e-degrees, Archive for Mathematical Logic, to appear.
[3]Cooper, S. B., Enumeration reducihility, 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-Verlag, Heidelberg, 1990, pp. 57110.
[4]Cooper, S. B., Enumeration reducihility, nondeterministic computations and relative computability of partial functions, Recursion theory week, Oberwolfach 1989 (Ambos-Spies, K., Muller, G., and Sacks, G. E., editors), Lecture Notes in Mathematics, vol. 1432, Springer-Verlag, Heildelberg, 1990, pp. 57110.
[5]Downey, R. G., d. r. e. degrees and the nondiamond theorem, Bulletin of the London Mathematical Society, vol. 21 (1989), pp. 4350.
[6]Rogers, H. Jr., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.
[7]Kalimullin, I. Sh., On elementary theories of n-c.e. enumeration degrees, Izvestija VUZov, Matematika, to appear (in Russian).
[8]Soare, R. I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Omega Series, Springer-Verlag, Heidelberg, 1987.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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