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The strong homogeneity conjecture

  • L. Feiner (a1)

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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].

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[1]Feiner, L., Degrees of non-recursive presentability, in preparation.
[2]Hugill, D., Initial segments of Turing degrees, Proceedings of the London Mathematical Society, vol. 19 (1969), pp. 115.
[3]Rogers, H., The theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.
[4]Yates, C., A survey of degrees (to appear).

The strong homogeneity conjecture

  • L. Feiner (a1)

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