| Title | Almost zero and high $\omega$-Turing degrees |
| Publication Type | Journal Article |
| Year of Publication | 2025 |
| Authors | Sariev A |
| Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
| Volume | 112 |
| Start Page | 137 |
| Pagination | 137-152 |
| ISSN | 1313-9215 (Print) 2603-5529 (Online) |
| 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. |
| DOI | 10.60063/GSU.FMI.112.137-152 |
| Attachment | Size |
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 112-137-152.pdf | 583.64 KB |