Almost zero and high $\omega$-Turing degrees

Authors

DOI:

https://doi.org/10.60063/gsu.fmi.112.137-152

Keywords:

definability, degree structures, Turing reducibility

Abstract

We show that the class of the high degrees is definable in the terms of the almost zero degrees in the local substructure of the $\omega$-Turing degrees. Namely, we prove that a degree is high if and only if it bounds all almost zero degrees.

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Published

2025-12-05

Issue

Vol. 112 (2025): Ann. Sofia Univ. Fac. Math. and Inf.

Section

Articles

How to Cite

Almost zero and high $\omega$-Turing degrees. (2025). Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 112, 137-152. https://doi.org/10.60063/gsu.fmi.112.137-152