DEFINABILITY OF JUMP CLASSES IN THE LOCAL THEORY OF THE $\omega$-ENUMERATION DEGREES

Authors

  • Hristo Ganchev
  • Andrey C. Sariev

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.

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Published

2015-12-12

How to Cite

Ganchev, H., & C. Sariev, A. (2015). DEFINABILITY OF JUMP CLASSES IN THE LOCAL THEORY OF THE $\omega$-ENUMERATION DEGREES. Ann. Sofia Univ. Fac. Math. And Inf., 102, 207–224. Retrieved from https://annual.uni-sofia.bg/index.php/fmi/article/view/70

Issue

Vol. 102 (2015): Ann. Sofia Univ. Fac. Math and Inf.

Section

Articles