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  1. A Guided Tour of Minimal Indices and Shortest Descriptions.Marcus Schaefer - 1998 - Archive for Mathematical Logic 37 (8):521-548.
    The set of minimal indices of a Gödel numbering $\varphi$ is defined as ${\rm MIN}_{\varphi} = \{e: (\forall i < e)[\varphi_i \neq \varphi_e]\}$ . It has been known since 1972 that ${\rm MIN}_{\varphi} \equiv_{\mathrm{T}} \emptyset^{\prime \prime }$ , but beyond this ${\rm MIN}_{\varphi}$ has remained mostly uninvestigated. This paper collects the scarce results on ${\rm MIN}_{\varphi}$ from the literature and adds some new observations including that ${\rm MIN}_{\varphi}$ is autoreducible, but neither regressive nor (1,2)-computable. We also study several variants of (...)
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  • Recursive Enumerability and the Jump Operator.Gerald E. Sacks - 1964 - Journal of Symbolic Logic 29 (4):204-204.
  • On the Size of Machines.[author unknown] - 1972 - Journal of Symbolic Logic 37 (1):199-200.
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  • Recursively Enumerable Sets Modulo Iterated Jumps and Extensions of Arslanov's Completeness Criterion.C. G. Jockusch, M. Lerman, R. I. Soare & R. M. Solovay - 1989 - Journal of Symbolic Logic 54 (4):1288-1323.
  • 1-Reducibility Inside an M-Degree with Maximal Set.E. Herrmann - 1992 - Journal of Symbolic Logic 57 (3):1046-1056.
    The structure of the l-degrees included in an m-degree with a maximal set together with the l-reducibility relation is characterized. For this a special sublattice of the lattice of recursively enumerable sets under the set-inclusion is used.
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