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An almost-universal cupping degree. (English) Zbl 1247.03077

Summary: Say that an incomplete d.r.e. degree has the almost universal cupping property, if it cups all the r.e. degrees not below it to \(\mathbf {0^\prime}\). In this paper, we construct such a degree \(\mathbf d\), with all the r.e. degrees not cupping \(\mathbf d\) to \(\mathbf {0^\prime}\) bounded by some r.e. degree strictly below \(\mathbf d\). The construction itself is an interesting \(\mathbf {0^{\prime \prime \prime}}\)-argument and this new structural property can be used to study final segments of various degree structures in the Ershov hierarchy.

MSC:

03D25 Recursively (computably) enumerable sets and degrees
03D55 Hierarchies of computability and definability
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[1] DOI: 10.1016/0168-0072(91)90005-7 · Zbl 0756.03020 · doi:10.1016/0168-0072(91)90005-7
[2] Izvestiya Vysshikh Uchebnykh Zavedeniǐ Matematika 7 pp 27– (1988)
[3] Doklady Akademiya Nauk SSSR. New Series 283 pp 270– (1985)
[4] Sets, models and recursion theory, Proceedings of the summer school in mathematical logic and tenth logic colloquium, Leicester, 1965 pp 264– (1967)
[5] Jump operator and Yates degrees 71 pp 252– (2006)
[6] Bi-isolation in the d.c.e. degrees 69 pp 409– (2004) · Zbl 1076.03028
[7] Isolated d.r.e. degrees pp 25– (1995)
[8] DOI: 10.1002/1521-3870(200111)47:4&lt;525::AID-MALQ525&gt;3.0.CO;2-7 · Zbl 1003.03039 · doi:10.1002/1521-3870(200111)47:4<525::AID-MALQ525>3.0.CO;2-7
[9] Complementation in the Turing degrees 54 pp 160– (1989)
[10] Recursively enumerable sets and degrees (1987)
[11] Classical recursion theory (1989)
[12] DOI: 10.1112/S002461159900163X · doi:10.1112/S002461159900163X
[13] Theory and applications of models of computation pp 721– (2006)
[14] Isolation and lattice embeddigs 67 pp 1055– (2002)
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