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The strong homogeneity conjecture

Published online by Cambridge University Press:  12 March 2014

L. Feiner
L. Feiner*
Affiliation:
State University of New York at Stony Brook
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Extract

The strong homogeneity conjecture asserts that, for any Turing degree, a, there is a jump preserving isomorphism from the upper semilattice of degrees to the upper semilattice of degrees above a. Rogers [3, p. 261] states that this problem is open and notes that its truth would simplify many proofs about degrees. It is, in fact, false. More precisely, let 0 be the smallest degree and let 0(n) be the nth iterated jump of 0, as defined in [3, pp. 254–256].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 3 , September 1970 , pp. 375 - 377
Copyright
Copyright © Association for Symbolic Logic 1971

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References

[1]Feiner, L., Degrees of non-recursive presentability, in preparation.Google Scholar
[2]Hugill, D., Initial segments of Turing degrees, Proceedings of the London Mathematical Society, vol. 19 (1969), pp. 1–15.CrossRefGoogle Scholar
[3]Rogers, H., The theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar
[4]Yates, C., A survey of degrees (to appear).Google Scholar