| Title | DEFINABILITY OF JUMP CLASSES IN THE LOCAL THEORY OF THE $\omega$-ENUMERATION DEGREES |
| Publication Type | Journal Article |
| Year of Publication | 2015 |
| Authors | Ganchev H, Sariev A |
| Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
| Volume | 102 |
| Pagination | 207-224 |
| ISSN | 0205-0808 |
| Keywords | $\omega$-enumeration degrees, definability, degree structures, enumeration reducibility, jump classes, local substructures |
| Abstract | In the present paper we continue the study of the definability in the local substructure $\mathcal{G}$ of the $\omega$-enumeration degrees, which was started in the work of Ganchev and Soskova [3]. We show that the class $\textbf{I}$ of the intermediate degrees is definable in $\mathcal{G}_\omega$. As a consequence of our observations, we show that the first jump of the least $\omega$-enumeration degree is also definable. |
| 2000 MSC | 03D28, 03D30 |
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 102-207-224.pdf | 245.32 KB |